Matrix multiplication worksheet for Algebra 2

Row times column, one entry at a time. The inner dimensions have to match, and the answer takes the outer ones: a 2x3 times a 3x2 gives a 2x2.

Also taught in Precalculus, at its own level and with its own examples.

Select your difficulty

Pick more than one for a sheet that mixes them.

The preview can look cramped on a phone. The PDF and printed sheet come out normal.



Sigma Prep · sigmaprep.io/worksheets Name Matrix Multiplication Date Period Multiply, or answer as asked. Multiply matrices $[\begin{array}{cc} - 6 & 4 \\ 5 & - 2 \end{array}] [\begin{array}{cc} - 3 & - 5 \\ - 4 & 3 \end{array}]$ $[\begin{array}{ccc} - 7 & 3 & 2 \\ - 4 & - 2 & 6 \end{array}] [\begin{array}{c} - 3 \\ - 6 \\ 3 \end{array}]$ $[\begin{array}{cc} 5 & 5 \\ - 3 & 1 \end{array}] [\begin{array}{cc} - 8 & 4 \\ 8 & 2 \end{array}]$ $[\begin{array}{cc} 6 & - 9 \\ - 8 & 6 \end{array}] [\begin{array}{cc} 6 & 9 \\ 8 & 4 \end{array}]$ $[\begin{array}{cc} - 9 & 4 \\ 4 & - 6 \end{array}] [\begin{array}{c} - 7 \\ - 1 \end{array}]$ $[\begin{array}{ccc} - 5 & 8 & - 5 \\ 2 & - 3 & - 4 \end{array}] [\begin{array}{c} 1 \\ 2 \\ 8 \end{array}]$ $[\begin{array}{cc} - 9 & - 6 \\ 1 & - 7 \end{array}] [\begin{array}{cc} 8 & - 5 \\ - 2 & 5 \end{array}]$ $[\begin{array}{cc} 6 & 7 \\ 9 & 6 \end{array}] [\begin{array}{c} - 2 \\ 4 \end{array}]$ $[\begin{array}{cc} - 7 & - 3 \\ 9 & - 5 \end{array}] [\begin{array}{cc} - 8 & - 9 \\ 6 & 2 \end{array}]$ $[\begin{array}{cc} 6 & 7 \\ 3 & 5 \end{array}] [\begin{array}{cc} - 5 & - 1 \\ - 7 & - 1 \end{array}]$ Find the dimensions of a product Matrix $A$ has 1 row and 2 columns and $B$ has 2 rows and 4 columns. Find the size of $A B$ and of $B A$ . Write undefined for a product that does not exist. Matrix $A$ is $1 \times 2$ and $B$ is $3 \times 3$ . For each of $A B$ and $B A$ , say whether the product exists and, if it does, give its dimensions. Matrix $A$ is $2 \times 2$ and $B$ is $4 \times 2$ . Determine the dimensions of the products $A B$ and $B A$ , writing undefined where a product does not exist. Matrix $A$ has 3 rows and 3 columns and $B$ has 4 rows and 3 columns. Which of $A B$ and $B A$ are defined? Give the dimensions of each, or write undefined. Matrix $A$ has 2 rows and 4 columns and $B$ has 4 rows and 2 columns. What size is $A B$ , and what size is $B A$ ? Write undefined if a product cannot be formed. Matrix $A$ has 3 rows and 4 columns and $B$ has 4 rows and 4 columns. Give the dimensions of $A B$ and $B A$ , or write undefined. Matrix $A$ is $2 \times 3$ and $B$ is $3 \times 2$ . Which of $A B$ and $B A$ are defined? Give the dimensions of each, or write undefined. Matrix $A$ is $4 \times 4$ and $B$ is $3 \times 4$ . What size is $A B$ , and what size is $B A$ ? Write undefined if a product cannot be formed. Matrix $A$ has 1 row and 3 columns and $B$ has 3 rows and 3 columns. For each of $A B$ and $B A$ , say whether the product exists and, if it does, give its dimensions. Matrix $A$ is $4 \times 3$ and $B$ is $3 \times 4$ . Give the dimensions of $A B$ and $B A$ , or write undefined. Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Matrix Multiplication

Date Period

Multiply, or answer as asked.

Multiply matrices
$[\begin{array}{cc} - 6 & 4 \\ 5 & - 2 \end{array}] [\begin{array}{cc} - 3 & - 5 \\ - 4 & 3 \end{array}]$
$[\begin{array}{ccc} - 7 & 3 & 2 \\ - 4 & - 2 & 6 \end{array}] [\begin{array}{c} - 3 \\ - 6 \\ 3 \end{array}]$
$[\begin{array}{cc} 5 & 5 \\ - 3 & 1 \end{array}] [\begin{array}{cc} - 8 & 4 \\ 8 & 2 \end{array}]$
$[\begin{array}{cc} 6 & - 9 \\ - 8 & 6 \end{array}] [\begin{array}{cc} 6 & 9 \\ 8 & 4 \end{array}]$
$[\begin{array}{cc} - 9 & 4 \\ 4 & - 6 \end{array}] [\begin{array}{c} - 7 \\ - 1 \end{array}]$
$[\begin{array}{ccc} - 5 & 8 & - 5 \\ 2 & - 3 & - 4 \end{array}] [\begin{array}{c} 1 \\ 2 \\ 8 \end{array}]$
$[\begin{array}{cc} - 9 & - 6 \\ 1 & - 7 \end{array}] [\begin{array}{cc} 8 & - 5 \\ - 2 & 5 \end{array}]$
$[\begin{array}{cc} 6 & 7 \\ 9 & 6 \end{array}] [\begin{array}{c} - 2 \\ 4 \end{array}]$
$[\begin{array}{cc} - 7 & - 3 \\ 9 & - 5 \end{array}] [\begin{array}{cc} - 8 & - 9 \\ 6 & 2 \end{array}]$
$[\begin{array}{cc} 6 & 7 \\ 3 & 5 \end{array}] [\begin{array}{cc} - 5 & - 1 \\ - 7 & - 1 \end{array}]$

Find the dimensions of a product
Matrix $A$ has 1 row and 2 columns and $B$ has 2 rows and 4 columns. Find the size of $A B$ and of $B A$ . Write undefined for a product that does not exist.
Matrix $A$ is $1 \times 2$ and $B$ is $3 \times 3$ . For each of $A B$ and $B A$ , say whether the product exists and, if it does, give its dimensions.
Matrix $A$ is $2 \times 2$ and $B$ is $4 \times 2$ . Determine the dimensions of the products $A B$ and $B A$ , writing undefined where a product does not exist.
Matrix $A$ has 3 rows and 3 columns and $B$ has 4 rows and 3 columns. Which of $A B$ and $B A$ are defined? Give the dimensions of each, or write undefined.
Matrix $A$ has 2 rows and 4 columns and $B$ has 4 rows and 2 columns. What size is $A B$ , and what size is $B A$ ? Write undefined if a product cannot be formed.
Matrix $A$ has 3 rows and 4 columns and $B$ has 4 rows and 4 columns. Give the dimensions of $A B$ and $B A$ , or write undefined.
Matrix $A$ is $2 \times 3$ and $B$ is $3 \times 2$ . Which of $A B$ and $B A$ are defined? Give the dimensions of each, or write undefined.
Matrix $A$ is $4 \times 4$ and $B$ is $3 \times 4$ . What size is $A B$ , and what size is $B A$ ? Write undefined if a product cannot be formed.
Matrix $A$ has 1 row and 3 columns and $B$ has 3 rows and 3 columns. For each of $A B$ and $B A$ , say whether the product exists and, if it does, give its dimensions.
Matrix $A$ is $4 \times 3$ and $B$ is $3 \times 4$ . Give the dimensions of $A B$ and $B A$ , or write undefined.



Sigma Prep · sigmaprep.io/worksheets Name Matrix MultiplicationAnswer keyVersion 1 Date Period Multiply, or answer as asked. Multiply matrices $[\begin{array}{cc} - 6 & 4 \\ 5 & - 2 \end{array}] [\begin{array}{cc} - 3 & - 5 \\ - 4 & 3 \end{array}]$ $[\begin{array}{cc} 2 & 42 \\ - 7 & - 31 \end{array}]$ $[\begin{array}{ccc} - 7 & 3 & 2 \\ - 4 & - 2 & 6 \end{array}] [\begin{array}{c} - 3 \\ - 6 \\ 3 \end{array}]$ $[\begin{array}{c} 9 \\ 42 \end{array}]$ $[\begin{array}{cc} 5 & 5 \\ - 3 & 1 \end{array}] [\begin{array}{cc} - 8 & 4 \\ 8 & 2 \end{array}]$ $[\begin{array}{cc} 0 & 30 \\ 32 & - 10 \end{array}]$ $[\begin{array}{cc} 6 & - 9 \\ - 8 & 6 \end{array}] [\begin{array}{cc} 6 & 9 \\ 8 & 4 \end{array}]$ $[\begin{array}{cc} - 36 & 18 \\ 0 & - 48 \end{array}]$ $[\begin{array}{cc} - 9 & 4 \\ 4 & - 6 \end{array}] [\begin{array}{c} - 7 \\ - 1 \end{array}]$ $[\begin{array}{c} 59 \\ - 22 \end{array}]$ $[\begin{array}{ccc} - 5 & 8 & - 5 \\ 2 & - 3 & - 4 \end{array}] [\begin{array}{c} 1 \\ 2 \\ 8 \end{array}]$ $[\begin{array}{c} - 29 \\ - 36 \end{array}]$ $[\begin{array}{cc} - 9 & - 6 \\ 1 & - 7 \end{array}] [\begin{array}{cc} 8 & - 5 \\ - 2 & 5 \end{array}]$ $[\begin{array}{cc} - 60 & 15 \\ 22 & - 40 \end{array}]$ $[\begin{array}{cc} 6 & 7 \\ 9 & 6 \end{array}] [\begin{array}{c} - 2 \\ 4 \end{array}]$ $[\begin{array}{c} 16 \\ 6 \end{array}]$ $[\begin{array}{cc} - 7 & - 3 \\ 9 & - 5 \end{array}] [\begin{array}{cc} - 8 & - 9 \\ 6 & 2 \end{array}]$ $[\begin{array}{cc} 38 & 57 \\ - 102 & - 91 \end{array}]$ $[\begin{array}{cc} 6 & 7 \\ 3 & 5 \end{array}] [\begin{array}{cc} - 5 & - 1 \\ - 7 & - 1 \end{array}]$ $[\begin{array}{cc} - 79 & - 13 \\ - 50 & - 8 \end{array}]$ Find the dimensions of a product Matrix $A$ has 1 row and 2 columns and $B$ has 2 rows and 4 columns. Find the size of $A B$ and of $B A$ . Write undefined for a product that does not exist. $A B$ : $1 \times 4$ ; $B A$ : undefined Matrix $A$ is $1 \times 2$ and $B$ is $3 \times 3$ . For each of $A B$ and $B A$ , say whether the product exists and, if it does, give its dimensions. $A B$ : undefined; $B A$ : undefined Matrix $A$ is $2 \times 2$ and $B$ is $4 \times 2$ . Determine the dimensions of the products $A B$ and $B A$ , writing undefined where a product does not exist. $A B$ : undefined; $B A$ : $4 \times 2$ Matrix $A$ has 3 rows and 3 columns and $B$ has 4 rows and 3 columns. Which of $A B$ and $B A$ are defined? Give the dimensions of each, or write undefined. $A B$ : undefined; $B A$ : $4 \times 3$ Matrix $A$ has 2 rows and 4 columns and $B$ has 4 rows and 2 columns. What size is $A B$ , and what size is $B A$ ? Write undefined if a product cannot be formed. $A B$ : $2 \times 2$ ; $B A$ : $4 \times 4$ Matrix $A$ has 3 rows and 4 columns and $B$ has 4 rows and 4 columns. Give the dimensions of $A B$ and $B A$ , or write undefined. $A B$ : $3 \times 4$ ; $B A$ : undefined Matrix $A$ is $2 \times 3$ and $B$ is $3 \times 2$ . Which of $A B$ and $B A$ are defined? Give the dimensions of each, or write undefined. $A B$ : $2 \times 2$ ; $B A$ : $3 \times 3$ Matrix $A$ is $4 \times 4$ and $B$ is $3 \times 4$ . What size is $A B$ , and what size is $B A$ ? Write undefined if a product cannot be formed. $A B$ : undefined; $B A$ : $3 \times 4$ Matrix $A$ has 1 row and 3 columns and $B$ has 3 rows and 3 columns. For each of $A B$ and $B A$ , say whether the product exists and, if it does, give its dimensions. $A B$ : $1 \times 3$ ; $B A$ : undefined Matrix $A$ is $4 \times 3$ and $B$ is $3 \times 4$ . Give the dimensions of $A B$ and $B A$ , or write undefined. $A B$ : $4 \times 4$ ; $B A$ : $3 \times 3$ Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Matrix MultiplicationAnswer keyVersion 1

Date Period

Multiply, or answer as asked.

Multiply matrices
$[\begin{array}{cc} - 6 & 4 \\ 5 & - 2 \end{array}] [\begin{array}{cc} - 3 & - 5 \\ - 4 & 3 \end{array}]$ $[\begin{array}{cc} 2 & 42 \\ - 7 & - 31 \end{array}]$
$[\begin{array}{ccc} - 7 & 3 & 2 \\ - 4 & - 2 & 6 \end{array}] [\begin{array}{c} - 3 \\ - 6 \\ 3 \end{array}]$ $[\begin{array}{c} 9 \\ 42 \end{array}]$
$[\begin{array}{cc} 5 & 5 \\ - 3 & 1 \end{array}] [\begin{array}{cc} - 8 & 4 \\ 8 & 2 \end{array}]$ $[\begin{array}{cc} 0 & 30 \\ 32 & - 10 \end{array}]$
$[\begin{array}{cc} 6 & - 9 \\ - 8 & 6 \end{array}] [\begin{array}{cc} 6 & 9 \\ 8 & 4 \end{array}]$ $[\begin{array}{cc} - 36 & 18 \\ 0 & - 48 \end{array}]$
$[\begin{array}{cc} - 9 & 4 \\ 4 & - 6 \end{array}] [\begin{array}{c} - 7 \\ - 1 \end{array}]$ $[\begin{array}{c} 59 \\ - 22 \end{array}]$
$[\begin{array}{ccc} - 5 & 8 & - 5 \\ 2 & - 3 & - 4 \end{array}] [\begin{array}{c} 1 \\ 2 \\ 8 \end{array}]$ $[\begin{array}{c} - 29 \\ - 36 \end{array}]$
$[\begin{array}{cc} - 9 & - 6 \\ 1 & - 7 \end{array}] [\begin{array}{cc} 8 & - 5 \\ - 2 & 5 \end{array}]$ $[\begin{array}{cc} - 60 & 15 \\ 22 & - 40 \end{array}]$
$[\begin{array}{cc} 6 & 7 \\ 9 & 6 \end{array}] [\begin{array}{c} - 2 \\ 4 \end{array}]$ $[\begin{array}{c} 16 \\ 6 \end{array}]$
$[\begin{array}{cc} - 7 & - 3 \\ 9 & - 5 \end{array}] [\begin{array}{cc} - 8 & - 9 \\ 6 & 2 \end{array}]$ $[\begin{array}{cc} 38 & 57 \\ - 102 & - 91 \end{array}]$
$[\begin{array}{cc} 6 & 7 \\ 3 & 5 \end{array}] [\begin{array}{cc} - 5 & - 1 \\ - 7 & - 1 \end{array}]$ $[\begin{array}{cc} - 79 & - 13 \\ - 50 & - 8 \end{array}]$

Find the dimensions of a product
Matrix $A$ has 1 row and 2 columns and $B$ has 2 rows and 4 columns. Find the size of $A B$ and of $B A$ . Write undefined for a product that does not exist. $A B$ : $1 \times 4$ ; $B A$ : undefined
Matrix $A$ is $1 \times 2$ and $B$ is $3 \times 3$ . For each of $A B$ and $B A$ , say whether the product exists and, if it does, give its dimensions. $A B$ : undefined; $B A$ : undefined
Matrix $A$ is $2 \times 2$ and $B$ is $4 \times 2$ . Determine the dimensions of the products $A B$ and $B A$ , writing undefined where a product does not exist. $A B$ : undefined; $B A$ : $4 \times 2$
Matrix $A$ has 3 rows and 3 columns and $B$ has 4 rows and 3 columns. Which of $A B$ and $B A$ are defined? Give the dimensions of each, or write undefined. $A B$ : undefined; $B A$ : $4 \times 3$
Matrix $A$ has 2 rows and 4 columns and $B$ has 4 rows and 2 columns. What size is $A B$ , and what size is $B A$ ? Write undefined if a product cannot be formed. $A B$ : $2 \times 2$ ; $B A$ : $4 \times 4$
Matrix $A$ has 3 rows and 4 columns and $B$ has 4 rows and 4 columns. Give the dimensions of $A B$ and $B A$ , or write undefined. $A B$ : $3 \times 4$ ; $B A$ : undefined
Matrix $A$ is $2 \times 3$ and $B$ is $3 \times 2$ . Which of $A B$ and $B A$ are defined? Give the dimensions of each, or write undefined. $A B$ : $2 \times 2$ ; $B A$ : $3 \times 3$
Matrix $A$ is $4 \times 4$ and $B$ is $3 \times 4$ . What size is $A B$ , and what size is $B A$ ? Write undefined if a product cannot be formed. $A B$ : undefined; $B A$ : $3 \times 4$
Matrix $A$ has 1 row and 3 columns and $B$ has 3 rows and 3 columns. For each of $A B$ and $B A$ , say whether the product exists and, if it does, give its dimensions. $A B$ : $1 \times 3$ ; $B A$ : undefined
Matrix $A$ is $4 \times 3$ and $B$ is $3 \times 4$ . Give the dimensions of $A B$ and $B A$ , or write undefined. $A B$ : $4 \times 4$ ; $B A$ : $3 \times 3$

How to do these

$[\begin{array}{cc} 1 & 2 \\ 3 & 4 \end{array}] [\begin{array}{c} 5 \\ 6 \end{array}]$

First row times the column: 1(5) + 2(6) = 17.
Second row times the column: 3(5) + 4(6) = 39.

The answer is $[\begin{array}{c} 17 \\ 39 \end{array}]$ .

Where students go wrong

Multiplying position by position, the way addition works. Matrix multiplication is rows against columns, and the order matters: AB and BA are usually different, and one of them may not even exist.

Also called multiplying matrices, matrix products or row by column multiplication.

What you can put on this worksheet

Multiplying two matrices: $[\begin{array}{cc} 2 & 3 \\ 4 & 1 \end{array}] [\begin{array}{cc} 3 & 5 \\ - 6 & 2 \end{array}]$ → $[\begin{array}{cc} - 12 & 16 \\ 6 & 22 \end{array}]$
Is the product defined? Its dimensions: Matrix $A$ is $1 \times 2$ and $B$ is $3 \times 3$ . Is the product $B A$ defined? If it is, give its size. → No
Undefined products, sums with products, letters, bigger sizes: $- 4 [\begin{array}{cc} - 4 & - 6 \\ - 6 & 6 \end{array}] [\begin{array}{c} - 4 \\ - 4 \end{array}]$ → $[\begin{array}{c} - 160 \\ 0 \end{array}]$
A product of three matrices: Find the product:
$[\begin{array}{cc} 1 & 2 \end{array}] [\begin{array}{cc} - 4 & 0 \\ 1 & - 2 \end{array}] [\begin{array}{c} 4 \\ - 1 \end{array}]$ → $[\begin{array}{c} - 4 \end{array}]$

Questions about these worksheets

Yes. Every matrix multiplication sheet is free to print and free to download as a PDF. There is no account to make, no email to hand over and no limit on how many you take.

Yes. The answer key prints on a second page, and you can choose whether it shows each question beside its answer or just the answers in a list.

Yes. Print straight from the page, or download the PDF and print that. The sheet is laid out for paper rather than squeezed off a screen, so there is room to work under each question, and the answer key comes out on its own page.

Algebra 2 is usually taken around 10th or 11th grade, though schools vary and plenty of students meet it earlier or later. Pick the difficulty rather than the grade: the easy level suits a first lesson on it, the hard level suits review before a test.

Yes, as many as you like. The questions are built fresh each time rather than picked from a fixed set of files, so pressing Generate gives a new sheet. That is what you want for a second class, a retake, or two students sitting next to each other.

That is the closest comparison, and Kuta Software is good software. It is also paid software you install on a computer. These worksheets run in a browser tab for free, with no account and nothing to install. Like Kuta, the matrix multiplication questions are generated when you ask for them rather than pulled from a fixed set of files, so two classes never get the same sheet, and the answer key comes with it.

Yes. There are three levels, and you can tick more than one for a sheet that mixes them, in which case the questions come out easiest first. The harder levels are not just larger numbers: they ask for something the easy ones do not.

You pick from 4: multiplying two matrices, is the product defined? its dimensions, undefined products, sums with products, letters, bigger sizes and a product of three matrices. Tick as many as you want and set how many of each, or let it spread them evenly.

Multiplying position by position, the way addition works. Matrix multiplication is rows against columns, and the order matters: AB and BA are usually different, and one of them may not even exist.

Matrix multiplication worksheet for Algebra 2

Select your difficulty

Multiply matrices

Find the dimensions of a product

Multiply matrices

Find the dimensions of a product

How to do these

Where students go wrong

What you can put on this worksheet

Questions about these worksheets

Are these matrix multiplication worksheets free?+

Do the matrix multiplication worksheets come with an answer key?+

Are these matrix multiplication worksheets printable?+

What grade are these matrix multiplication worksheets for?+

Can I get a different version of the same matrix multiplication worksheet?+

Is this a free alternative to Kuta Software for matrix multiplication?+

Can I choose how hard the matrix multiplication questions are?+

What kinds of question are on a matrix multiplication worksheet?+

What do students get wrong with matrix multiplication?+