Chapter 3 - Determinants - 3.2 Exercises - Page 178: 36

$ r^n \det A$

\begin{align*} & \quad\det{(rA)} \\ & = \begin{vmatrix} r\mathbf{A}_1 \\ \cdots \\ r\mathbf{A}_n \end{vmatrix} \\ & = r^n \begin{vmatrix} \mathbf{A}_1 \\ \cdots \\ \mathbf{A}_n \end{vmatrix} \\ & = r^n \det A \end{align*}