Worksheets · Precalculus

Inverse matrices worksheet for Precalculus

Precalculus inverses include determinants other than 1, so fractions appear in the answer, and singular matrices with determinant 0, which have no inverse at all. The inverse is the tool for solving matrix equations next, so check each one by multiplying back to the identity.

Also taught in Algebra 2, at its own level and with its own examples.

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Pick more than one for a sheet that mixes them.

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

Sigma Prep · sigmaprep.io/worksheets

Name

Inverse Matrices

Date Period

Find the inverse of each matrix, or answer as asked.

  1. Find the inverse of a 2×22 \times 2 matrix

    [ 6−7−11 ]
  2. [ −4−5−7−9 ]
  3. [ 1−48−31 ]
  4. [ 171178 ]
  5. [ 16−4−23 ]
  6. [ −924−1 ]
  7. [ −2−537 ]
  8. [ −73−125 ]
  9. [ 16425 ]
  10. [ 14−11−43 ]

  1. Find the inverse, if it exists

    Find the inverse, if it exists: [ 3446 ]
  2. Find the inverse, if it exists: [ −2−5−16 ]
  3. Find the inverse, if it exists: [ 4−3−86 ]
  4. Find the inverse, if it exists: [ 1−515 ]
  5. Find the inverse, if it exists: [ −3−2−2−3 ]
  6. Find the inverse, if it exists: [ 42−8−4 ]
  7. Find the inverse, if it exists: [ 85−21 ]
  8. Find the inverse, if it exists: [ 4−41−5 ]
  9. Find the inverse, if it exists: [ −20−67 ]
  10. Find the inverse, if it exists: [ −210−3 ]

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

Sigma Prep · sigmaprep.io/worksheets

Name

Inverse MatricesAnswer keyVersion 2

Date Period

Find the inverse of each matrix, or answer as asked.

  1. Find the inverse of a 2×22 \times 2 matrix

    [ 6−7−11 ][ −1−7−1−6 ]
  2. [ −4−5−7−9 ][ −957−4 ]
  3. [ 1−48−31 ][ −314−81 ]
  4. [ 171178 ][ 78−7−111 ]
  5. [ 16−4−23 ][ −23−641 ]
  6. [ −924−1 ][ −1−2−4−9 ]
  7. [ −2−537 ][ 75−3−2 ]
  8. [ −73−125 ][ 5−312−7 ]
  9. [ 16425 ][ 25−6−41 ]
  10. [ 14−11−43 ][ −43−4111 ]

  1. Find the inverse, if it exists

    Find the inverse, if it exists: [ 3446 ][ 3−2−232 ]
  2. Find the inverse, if it exists: [ −2−5−16 ][ −617−517−117217 ]
  3. Find the inverse, if it exists: [ 4−3−86 ]No inverse (the determinant is 0)
  4. Find the inverse, if it exists: [ 1−515 ][ 1212−110110 ]
  5. Find the inverse, if it exists: [ −3−2−2−3 ][ −352525−35 ]
  6. Find the inverse, if it exists: [ 42−8−4 ]No inverse (the determinant is 0)
  7. Find the inverse, if it exists: [ 85−21 ][ 118−5181949 ]
  8. Find the inverse, if it exists: [ 4−41−5 ][ 516−14116−14 ]
  9. Find the inverse, if it exists: [ −20−67 ][ −120−3717 ]
  10. Find the inverse, if it exists: [ −210−3 ][ −12−160−13 ]

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

How to do these

Find the inverse, if it exists: [ 4232 ]

  1. The determinant is 4(2) - 2(3) = 2, which is not 0, so an inverse exists.
  2. Swap the 4 and the 2 on the main diagonal and negate the other two: rows 2, -2 and -3, 4.
  3. Divide every entry by 2.

The answer is [ 1−1−322 ].

Where students go wrong

Skipping the determinant check. A matrix like rows 2, 4 and 1, 2 has determinant 0, so it has no inverse, and swapping and negating anyway produces a matrix that does not multiply back to the identity.

Also called finding the inverse of a matrix, 2x2 inverse or matrix inverses.

What you can put on this worksheet

The inverse of a 2x2
[ −3−4−4−5 ] → [ 5−4−43 ]
No inverse, or fractions
Find the inverse, if it exists: [ −5−1102 ] → No inverse (the determinant is 0)
Does a 3x3 inverse exist?
Does the inverse exist? [ 012−401−24−1 ] → Yes: the determinant is −38
3x3 inverses
Find the inverse: [ 3−22−11−1101 ] → [ 120011−1−21 ]
For which x is it invertible?
For which values of x is [ x+2−61x−3 ] invertible? → Every x except 0 and 1

Questions about these worksheets

Yes. Every inverse matrices 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 inverse matrices 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 5: the inverse of a 2x2, no inverse, or fractions, does a 3x3 inverse exist?, 3x3 inverses and for which x is it invertible?. Tick as many as you want and set how many of each, or let it spread them evenly.

Swapping the wrong pair. The two on the main diagonal trade places; the other two stay put and change sign. Getting that backwards gives a matrix that looks plausible and is not the inverse.