Show how to find the inverse of the matrix \(A= \left[\begin{array}{cccc} 1 & 0 & 0 & -1 \\ 1 & 1 & -2 & -7 \\ 3 & 0 & 1 & 2 \\ 5 & 0 & 0 & -4 \end{array}\right] \).
Answer:
\[A^{-1}= \left[\begin{array}{cccc} -4 & 0 & 0 & 1 \\ 13 & 1 & 2 & -4 \\ 22 & 0 & 1 & -5 \\ -5 & 0 & 0 & 1 \end{array}\right] \]