\begin{exercise}{G2}{Determinants}{0011}
\begin{exerciseStatement}
Show how to compute the determinant of the matrix \[A= \left[\begin{array}{cccc}
1 & 2 & -2 & 3 \\
3 & 0 & 0 & 0 \\
-6 & -1 & -4 & 3 \\
6 & -4 & 2 & -1
\end{array}\right] .\].
\end{exerciseStatement}
\begin{exerciseAnswer}\[\operatorname{det}\ \left[\begin{array}{cccc}
1 & 2 & -2 & 3 \\
3 & 0 & 0 & 0 \\
-6 & -1 & -4 & 3 \\
6 & -4 & 2 & -1
\end{array}\right] = 96 \]\end{exerciseAnswer}
\end{exercise}