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