Matrix Inverse, Determinant & Rank

Compute the determinant, rank, nullity, and inverse of a square matrix using Gaussian elimination with partial pivoting. Intermediate matrices are shown at each major step.

⊞ Input Matrix

Matrix size (n × n)

Or paste matrix (space/comma separated rows, newline between)

✓ Results

Enter a matrix and click Solve.

▸ How it works

Determinant is computed via Gaussian elimination: the product of the diagonal pivots (accounting for row swaps).

Rank is the number of non-zero pivots after reduction to row-echelon form.

Inverse (when it exists) is obtained by augmenting the matrix with the identity and reducing the left side to I; the right side becomes A⁻¹.

Partial pivoting is used for numerical stability. All arithmetic is floating-point; results are rounded for display.