Matrix Determinant — Gaussian Elimination

Reduce A to upper-triangular; det(A) = sign × product of pivots. Row-adds don't change det; each row swap flips the sign. Edit the matrix below and step through.

step 0

Matrix (editable) — working copy A

pivot pivot row row being eliminated
det = sign × ∏ pivots = ?

Running determinant

sign (flips on each row swap)+1
pivot product so far1
row swaps so far0
pivots collected:
(none yet)
why this step is valid:
press Step to begin
Press Step to begin. We eliminate column by column to reach upper-triangular form, then read det = sign × product of the diagonal pivots.
Self-contained visualization. Exact integer arithmetic (no rounding). Row operation "add a multiple of one row to another" leaves det unchanged; a row swap multiplies det by −1. See junior.md for the worked example and professional.md for the proof that det(A) = (−1)swaps × ∏ pivots.