Show how to compute the determinant of the matrix
\[A= \left[\begin{array}{cccc} 5 & 0 & 1 & 1 \\ -6 & -5 & -3 & 0 \\ 2 & 3 & 6 & -2 \\ -6 & 1 & -1 & 0 \end{array}\right] .\]
.Answer:
\[\operatorname{det}\ \left[\begin{array}{cccc} 5 & 0 & 1 & 1 \\ -6 & -5 & -3 & 0 \\ 2 & 3 & 6 & -2 \\ -6 & 1 & -1 & 0 \end{array}\right] = -156 \]