행렬 $A= \begin{bmatrix*}[r] 1 & 0 & 3 & 0 & 1 \\ 0 & 2 & 0 & 1 & 0 \\ 0 & 0 & 2 & 0 & 3 \\ 0 & 0 & 0 & 1 & 1 \\ 1 & -1 & 3 & -1 & 1 \end{bmatrix*}$ 의 $\det (A)$ 를 구하시오.

• ①$2$
• ②$4$
• ③$12$
• ④$18$