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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.
- 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.