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.
Worked examples
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Key terms
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.