Mr. Integral
Math notes/Linear Algebra/Linear Transformations

Determinants, Orientation and Invertibility — Cheat sheet

CHEAT SHEET   ·   FREE

Choose “Save as PDF” in the print dialog.
On this page

Core rule

det⁡(AB)=det⁡Adet⁡B\det(AB)=\det A\det B. Row swap: negate. Row scale: scale. Add a row multiple: unchanged. Triangular determinant: diagonal product.

Watch for

Determinants apply to square matrices. Magnitude measures volume scaling, not by itself numerical conditioning.