Last updated October 12, 2026 · Report an error
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.
Frequently asked questions
Yes, with no signup and no limit on how many calculations you run.
The inverse equals the adjugate divided by the determinant: \(A^{-1} = \text{adj}(A) / \det(A)\). This only works when the determinant is nonzero.
The adjugate is simply the transpose of the cofactor matrix — every entry swaps row and column position compared to the cofactor matrix.
Yes — the adjugate itself is always defined for a square matrix, even when the determinant is zero. It's only the division step (finding the inverse) that fails in that case.