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