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Matrix Inverse Calculator

Find the inverse of a 2x2 or 3x3 matrix. Singular matrices are detected and reported.

Matrix Inverse

Pick a size and fill the grid. Results update live.

Inverse
A^-1

Edit the grid to compute.

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Determinant
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Formula: A^-1 = adj(A) / det(A). The adjugate is the transpose of the cofactor matrix. A zero determinant means no inverse exists.
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Adjugate over determinant

The inverse is the adjugate matrix divided by the determinant. For 2x2 the tool swaps the diagonal, negates the off-diagonal, and divides by ad - bc. For 3x3 it builds the full cofactor matrix, transposes it, and divides by the 3x3 determinant.

Why singularity matters

A zero determinant means the matrix squashes space flat, so no inverse can undo it. The tool checks this first and reports a singular matrix instead of dividing by zero, which also tells you the related linear system has no unique solution.

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Matrix Inverse FAQs

What is the inverse of [[4,7],[2,6]]?
The determinant is 10, so the inverse is [[0.6,-0.7],[-0.2,0.4]]. Select 2 x 2; this matrix is preloaded.
How do I verify an inverse?
Multiply the matrix by its inverse: you should get the identity matrix with 1s on the diagonal and 0s elsewhere. Use the matrix multiplication tool for the check.
What does singular matrix mean?
It means the determinant is zero, so no inverse exists. Try [[1,2],[2,4]] to see the warning.
What is the inverse of the identity matrix?
The identity matrix itself. Enter 1s on the diagonal and 0s elsewhere to confirm.
Are my entries sent anywhere?
No. The adjugate computation runs fully in your browser.
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