Determinants and inverses

The determinant of a matrix is a single number that tells you how it scales area (or volume) and whether it can be undone. The inverse matrix undoes the transformation.

Key facts

• 2 × 2: det [[a, b], [c, d]] = ad − bc.
• |det| is the area scale factor; a negative determinant means a reflection.
• A⁻¹ = (1/det)[[d, −b], [−c, a]].
• If det = 0 the matrix has no inverse (it squashes space flat).

Worked examples