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The adjugate matrix (also called the classical adjoint) is the final building block needed before dividing by the determinant to find a matrix inverse.
This calculator finds the adjugate of a 2×2 up to 6×6 matrix by computing its cofactor matrix and transposing it.
How it works
Choose a matrix size and enter the matrix elements. The calculator first builds the cofactor matrix (the signed determinant of each minor), then transposes it — swapping rows and columns — to get the adjugate.
- Click Calculate to see your results.
Examples
A 2×2 example
For the matrix [[1, 2], [3, 4]], the adjugate is [[4, -2], [-3, 1]].
Who should use it
- Coursework involving matrix inverses or the adjugate method.
- Quickly checking a hand-calculated adjugate matrix.
Industry applications
- Linear algebra and mathematics education
- Engineering and applied mathematics
Advantages
- Shows both the cofactor matrix and the final transposed adjugate.
- A direct step toward finding a matrix inverse by hand.
Limitations
- Limited to square matrices up to 6×6.
Common mistakes to avoid
- Forgetting the transpose step and stopping at the cofactor matrix instead of the adjugate.
- Assuming the adjugate itself requires a nonzero determinant — only the inverse calculation (adjugate ÷ determinant) does.
Best practices
- Compute the cofactor matrix carefully first (getting every sign right), since the adjugate is just its transpose — an error in the cofactor step carries straight through.
Tips
- If you also need the matrix inverse itself, this site's Matrix Calculator computes the full inverse (adjugate divided by determinant) in one step.