Show how to find the inverse of the matrix \(P= \left[\begin{array}{cccc} 1 & -1 & 5 & 4 \\ 1 & 0 & 4 & 0 \\ -1 & 1 & -4 & -3 \\ -1 & -1 & -6 & 2 \end{array}\right] \).
Answer:
\[P^{-1}= \left[\begin{array}{cccc} 4 & 9 & 8 & 4 \\ 6 & 7 & 10 & 3 \\ -1 & -2 & -2 & -1 \\ 2 & 2 & 3 & 1 \end{array}\right] \]