Show how to compute the determinant of the matrix
\[A= \left[\begin{array}{cccc} -5 & -3 & 2 & -3 \\ -4 & 5 & 1 & -2 \\ 6 & -6 & 5 & 0 \\ 0 & 0 & 1 & -2 \end{array}\right] .\]
.Answer:
\[\operatorname{det}\ \left[\begin{array}{cccc} -5 & -3 & 2 & -3 \\ -4 & 5 & 1 & -2 \\ 6 & -6 & 5 & 0 \\ 0 & 0 & 1 & -2 \end{array}\right] = 376 \]