Answer
See below
Work Step by Step
Given $$ A=\left[ \begin{array}{cccc}{-1} & {2} & {0} & {0} \\ {2} & {-8} & {0} & {0} \\ {0} & {0} & {2} & {3} \\ {0} & {0} & {-1} & {-1}\end{array} \right]$$
So, we get
$det (A)=\begin{vmatrix} -1 & 2 & 0 & 0\\ 2 & -8 & 0 & 0\\ 0 & 0 & 2 & 3 \\ 0 & 0 & -1 & -1 \end{vmatrix}\\
=\begin{vmatrix}
-1 & 2 \\ 2 & -8
\end{vmatrix}.\begin{vmatrix}
2 & 3 \\ -1 & -1
\end{vmatrix}\\
=(-1.(-8)-2.2).(2.(-1)-3.(-1))\\
=4.1\\
=4$
