Inverse and Determinant Calculator with Steps

The determinant of an n×n matrix A can be defined by cofactor expansion or as the signed product of pivots during elimination. For 2×2:

det(A) = a₁₁a₂₂ − a₁₂a₂₁

The inverse exists only if det(A) ≠ 0. In general we compute A⁻¹ via Gauss–Jordan on the augmented matrix [A | I], performing row operations until the left side becomes I, yielding [I | A⁻¹]. For 2×2:

A⁻¹ = (1/det(A)) · [[a₂₂, −a₁₂], [−a₂₁, a₁₁]]

The implemented method uses partial pivoting for stability; the determinant equals the product of pivot elements with a sign correction for row swaps.

1. Select matrix size (2×2 up to 6×6).
2. Enter values directly, paste comma-separated rows, or use “Fill Random.”
3. Click Calculate to compute determinant, rank, and inverse (if invertible).
4. Open the Steps section to follow each row operation.
5. Use Download CSV for a spreadsheet-ready export of inputs and results.
6. Use Save/Print as PDF to export a nicely formatted report.