Determinant of Rescaling Matrix/Corollary

Theorem
Let $\mathbf A$ be a square matrix of order $n$.

Let $\lambda$ be a scalar.

Let $\lambda \mathbf A$ denote the scalar product of $\mathbf A$ by $\lambda$.

Then:


 * $\map \det {\lambda \mathbf A} = \lambda^n \map \det {\mathbf A}$

where $\det$ denotes determinant.