Worksheets · Precalculus

Matrix multiplication worksheet for Precalculus

In Precalculus the products get bigger, up to 3x3 times 3x3, and the size question comes before any arithmetic: does AB exist, does BA, and what shape is each. Multiplication is the engine behind inverses and transformations later in the unit, so the row-by-column habit needs to be automatic.

Also taught in Algebra 2, 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.

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.

  1. Multiply matrices

    [ 6−10−10−67−9 ][ −12−11−2−1612 ]
  2. [ 11281114 ][ 12−5−12−6116 ]
  3. [ −5−12−8−1226 ][ 5−10−6−10−6−2 ]
  4. [ 9−5129511 ][ 10584−7−9124−1 ]
  5. [ −3−10−121−5−3−6−2−1 ][ 21074−1110 ]
  6. [ 1110−9−128 ][ −2−94−956 ]
  7. [ −11−12−88−4−16−1−12 ][ −11−6−1211−4−1 ]
  8. [ −31111−2114 ][ −8−399 ]
  9. [ −1−85−8−5−8−7117 ][ 312−104−7−8 ]
  10. [ 10−10129−712 ][ −68−6−11−3−109−11−12 ]

  1. Find the dimensions of a product

    Let A=[ −597−5 ] and B=[ 9−492−35 ]. Give the dimensions of AB and BA, or write undefined.
  2. Let A=[ 94−439−5 ] and B=[ 32 ]. What size is AB, and what size is BA? Write undefined if a product cannot be formed.
  3. Let A=[ 571−3−2848−17548−520 ] and B=[ 2−45 ]. Which of AB and BA are defined? Give the dimensions of each, or write undefined.
  4. Let A=[ −4−193 ] and B=[ 9777 ]. For each of AB and BA, say whether the product exists and, if it does, give its dimensions.
  5. Let A=[ 2−35 ] and B=[ 3543−1−5930 ]. Find the size of AB and of BA. Write undefined for a product that does not exist.
  6. Let A=[ −263 ] and B=[ −1−3−4−4451−3−4 ]. Determine the dimensions of the products AB and BA, writing undefined where a product does not exist.
  7. Let A=[ −40−4−50−4−24 ] and B=[ 7−4−4357−32 ]. Which of AB and BA are defined? Give the dimensions of each, or write undefined.
  8. Let A=[ 365−329−3−3 ] and B=[ 234673616−1−51−1−2−17 ]. For each of AB and BA, say whether the product exists and, if it does, give its dimensions.
  9. Let A=[ 63−11 ] and B=[ 2580768−5 ]. Find the size of AB and of BA. Write undefined for a product that does not exist.
  10. Let A=[ 73−18 ] and B=[ 4−37−4 ]. Determine the dimensions of the products AB and BA, writing undefined where a product does not exist.

Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Matrix MultiplicationAnswer keyVersion 2

Date Period

Multiply, or answer as asked.

  1. Multiply matrices

    [ 6−10−10−67−9 ][ −12−11−2−1612 ][ −62−126−13212674−52−75−131−122 ]
  2. [ 11281114 ][ 12−5−12−6116 ][ −44−29−76−47 ]
  3. [ −5−12−8−1226 ][ 5−10−6−10−6−2 ][ 95186−10888 ]
  4. [ 9−5129511 ][ 10584−7−9124−1 ][ 2141281052425416 ]
  5. [ −3−10−121−5−3−6−2−1 ][ 21074−1110 ][ 56−1900−40−15−78 ]
  6. [ 1110−9−128 ][ −2−94−956 ][ 524210237 ]
  7. [ −11−12−88−4−16−1−12 ][ −11−6−1211−4−1 ][ 297−58−36−91−6−35 ]
  8. [ −31111−2114 ][ −8−399 ][ 123108−106−51−523 ]
  9. [ −1−85−8−5−8−7117 ][ 312−104−7−8 ][ 42−8482−52−180−96 ]
  10. [ 10−10129−712 ][ −68−6−11−3−109−11−12 ][ 158−22−104131−39−128 ]

  1. Find the dimensions of a product

    Let A=[ −597−5 ] and B=[ 9−492−35 ]. Give the dimensions of AB and BA, or write undefined.AB: 2×3; BA: undefined
  2. Let A=[ 94−439−5 ] and B=[ 32 ]. What size is AB, and what size is BA? Write undefined if a product cannot be formed.AB: undefined; BA: 1×3
  3. Let A=[ 571−3−2848−17548−520 ] and B=[ 2−45 ]. Which of AB and BA are defined? Give the dimensions of each, or write undefined.AB: undefined; BA: undefined
  4. Let A=[ −4−193 ] and B=[ 9777 ]. For each of AB and BA, say whether the product exists and, if it does, give its dimensions.AB: 1×1; BA: 4×4
  5. Let A=[ 2−35 ] and B=[ 3543−1−5930 ]. Find the size of AB and of BA. Write undefined for a product that does not exist.AB: 1×3; BA: undefined
  6. Let A=[ −263 ] and B=[ −1−3−4−4451−3−4 ]. Determine the dimensions of the products AB and BA, writing undefined where a product does not exist.AB: undefined; BA: 3×1
  7. Let A=[ −40−4−50−4−24 ] and B=[ 7−4−4357−32 ]. Which of AB and BA are defined? Give the dimensions of each, or write undefined.AB: 4×4; BA: 2×2
  8. Let A=[ 365−329−3−3 ] and B=[ 234673616−1−51−1−2−17 ]. For each of AB and BA, say whether the product exists and, if it does, give its dimensions.AB: 2×4; BA: undefined
  9. Let A=[ 63−11 ] and B=[ 2580768−5 ]. Find the size of AB and of BA. Write undefined for a product that does not exist.AB: undefined; BA: 4×2
  10. Let A=[ 73−18 ] and B=[ 4−37−4 ]. Determine the dimensions of the products AB and BA, writing undefined where a product does not exist.AB: 4×4; BA: 1×1

Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

How to do these

[ 102−131 ][ 312110 ]

  1. A 2x3 times a 3x2: the inner 3s match, so the product is 2x2.
  2. Row 1 times column 1: 1(3) + 0(2) + 2(1) = 5, and row 1 times column 2: 1(1) + 0(1) + 2(0) = 1.
  3. Row 2 gives -1(3) + 3(2) + 1(1) = 4 and -1(1) + 3(1) + 1(0) = 2.

The answer is [ 5142 ].

Where students go wrong

Taking the size of the product from the inner numbers instead of the outer ones. A 1x4 times a 4x1 is a 1x1, a single number, not a 4x4.

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

What you can put on this worksheet

Multiplying two matrices
[ 2341 ][ 35−62 ] → [ −1216622 ]
Is the product defined? Its dimensions
Matrix A is 1×2 and B is 3×3. Is the product BA defined? If it is, give its size. → No
Undefined products, sums with products, letters, bigger sizes
−4[ −4−6−66 ][ −4−4 ] → [ −1600 ]
A product of three matrices
Find the product:
[ 12 ][ −401−2 ][ 4−1 ] → [ −4 ]

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.

Precalculus is usually taken around 11th or 12th 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.