Linear Algebra
Advanced

Determinant of a Product

The determinant of a product is the product of determinants.

Formula

det⁡(AB)=det⁡(A)det⁡(B)\det(AB) = \det(A)\det(B)

Variables

A,BSquare matrices

Example

Multiplicative property

Did You Know?

A zero determinant signals a singular matrix that has no inverse and squashes space into a lower dimension.

matrixdeterminant