Show how to find the inverse of the matrix \(M= \left[\begin{array}{cccc} -3 & 1 & -1 & -1 \\ -1 & 0 & 0 & 1 \\ 1 & 1 & 4 & 8 \\ -2 & 0 & -2 & -3 \end{array}\right] \).
Answer:
\[M^{-1}= \left[\begin{array}{cccc} -2 & -3 & 2 & 5 \\ -2 & -5 & 3 & 7 \\ 5 & 6 & -5 & -13 \\ -2 & -2 & 2 & 5 \end{array}\right] \]