Skip to content
D DocNectar

Free Cofactor Matrix Calculator

Calculate the cofactor matrix of a 2×2 up to 6×6 matrix, a key building block for finding a matrix inverse.

100% Free No Signup Works on all devices

Built and fact-checked by the DocNectar team — see our editorial standards

Thanks for rating!

Key Features

Instant Calculation

Get accurate results in real time with our optimized algorithm.

Mobile Friendly

Fully responsive design. Works on all devices & screen sizes.

Privacy Focused

Your data stays on your device. We don't store any inputs.

100% Free

No hidden costs. This tool is completely free forever.

The cofactor matrix is a key intermediate step in finding a matrix's adjugate and inverse by hand, but computing every minor determinant and sign is tedious to do manually.

This calculator finds the full cofactor matrix of a 2×2 up to 6×6 matrix.

How it works

Choose a matrix size and enter the matrix elements. For each position, the calculator removes that row and column to form a minor matrix, finds its determinant, and multiplies by an alternating +/- sign based on position to get that entry's cofactor.

  1. Click Calculate to see your results.

Examples

A 2×2 example

For the matrix [[1, 2], [3, 4]], the cofactor matrix is [[4, -3], [-2, 1]].

Who should use it

  • Coursework involving matrix inverses, adjugates, or determinants.
  • Quickly checking a hand-calculated cofactor matrix.

Industry applications

  • Linear algebra and mathematics education
  • Engineering and applied mathematics

Advantages

  • Shows every minor determinant and sign used to build the result.
  • A direct building block toward finding a matrix inverse.

Limitations

  • Limited to square matrices up to 6×6.

Common mistakes to avoid

  • Forgetting to apply the alternating sign to each minor determinant.
  • Confusing the cofactor matrix with the adjugate matrix, which is its transpose.

Best practices

  • Work through the minors systematically, one position at a time, and double-check the sign pattern (+ - + / - + - / + - +) as you go.

Tips

  • If you also need the matrix inverse, this site's Matrix Calculator computes the full inverse (via the adjugate and determinant) in one step — this tool is useful when you specifically need to see the cofactor matrix on its own.

Frequently asked questions

Yes, with no signup and no limit on how many calculations you run.
Cofactors are used to compute a matrix's adjugate (by transposing the cofactor matrix) and, from there, its inverse — they're also used directly in cofactor-expansion determinant calculations.
The sign alternates in a checkerboard pattern based on position: C_{ij} uses (-1)^(i+j), so positions where i+j is even are positive and where i+j is odd are negative.
The adjugate is the transpose of the cofactor matrix — this tool shows the cofactor matrix itself, before that final transpose step.

Get new calculators and guides in your inbox

No spam — just new tools like Cofactor Matrix Calculator and practical guides.

Favorites