Answer
$ r^n \det A$
Work Step by Step
\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*}