Matrix Inverse Calculator
Find the inverse of a square matrix using the augmented matrix method . Supports matrices up to 8×8 with full step-by-step solutions for sizes ≤ 5.
Input Matrix
×3
Examples
Result
Enter a square matrix and click Find Inverse
2×2 Formula
For a 2×2 matrix, the inverse is computed directly using the formula: swap the diagonal, negate the off-diagonal, and divide by the determinant.
Row Reduction
For larger matrices, we augment with the identity matrix and row-reduce. When the left side becomes , the right side is .
Invertibility
A matrix is invertible if and only if its determinant is nonzero, or equivalently, its RREF is the identity matrix.