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