Matrix Inverse Calculator

Summary

Compute the inverse of a 2x2 or 3x3 matrix with step-by-step determinant and adjugate working.

How it works

1. Select the matrix size (2x2 or 3x3) from the toggle.
2. Fill in all matrix entries in the grid.
3. Click "Calculate Inverse" to run the computation.
4. The tool first computes the determinant; if it is zero, the matrix has no inverse.
5. For a non-singular matrix it builds the cofactor matrix, transposes it to get the adjugate, then divides by the determinant.
6. All intermediate steps are shown so you can follow the full derivation.

Use cases

• Check your manual matrix inversion homework.
• Solve systems of linear equations using the inverse method.
• Verify transformation matrix inverses in computer graphics.
• Explore invertibility conditions in linear algebra courses.
• Quickly invert rotation or scaling matrices for 2D/3D work.

Frequently Asked Questions