Linear Algebra

Matrix Inverse

The inverse of a square matrix A is the matrix A⁻¹ such that A·A⁻¹ is the identity. This calculator checks that the determinant is non-zero, then applies Gauss-Jordan elimination to produce the inverse.

Matrix Inverse

Inverse of a square matrix via Gauss-Jordan.

Try:

Frequently asked questions

Which matrices have an inverse?

Only square matrices with a non-zero determinant are invertible; a determinant of 0 means no inverse exists.

How is the inverse computed?

The matrix is augmented with the identity, then row-reduced; the identity side becomes the inverse.

Why check the determinant first?

A zero determinant signals a singular matrix, so the calculator can report cleanly that no inverse exists.