Show how to find the inverse of the matrix \(P= \left[\begin{array}{cccc} 1 & -1 & 0 & 1 \\ -5 & 6 & 1 & -1 \\ 3 & -6 & -2 & -4 \\ 4 & -5 & -2 & -4 \end{array}\right] \).
Answer:
\[P^{-1}= \left[\begin{array}{cccc} -6 & -2 & -1 & 0 \\ 6 & 2 & 0 & 1 \\ -53 & -17 & -4 & -5 \\ 13 & 4 & 1 & 1 \end{array}\right] \]