Answer
$$0$$
Work Step by Step
Given: $$\begin{array}{c}{A=\left[\begin{array}{ccc}{0} & {1} & {-2} \\ {-1} & {0} & {3} \\ {2} & {-3} & {0} \end{array}\right] }\end{array}=- \begin{vmatrix}{-1} & {0} & {3} \\ {0} & {1} & {-2} \\ {2} & {-3} & {0}\end{vmatrix}$$
Perform row operations $R_3 \rightarrow R_3+2R_1$ and $R_3 \rightarrow R_3+3R_2$ to obtain:
$$A=- \begin{vmatrix}{-1} & {0} & {3} \\ {0} & {1} & {-2} \\ {0} & {0} & {0}\end{vmatrix}$$
Determinant of triangular matrix is the product of its diagonal elements, so: $det (A)=-(1)(1)(0)=0$
