Show how to find the inverse of the matrix \(B= \left[\begin{array}{cccc} -1 & 0 & 2 & 2 \\ -1 & -1 & 4 & 2 \\ 0 & -1 & 5 & 8 \\ -1 & -1 & 5 & 5 \end{array}\right] \).
Answer:
\[B^{-1}= \left[\begin{array}{cccc} 3 & 6 & 4 & -10 \\ 7 & 9 & 6 & -16 \\ 3 & 5 & 3 & -8 \\ -1 & -2 & -1 & 3 \end{array}\right] \]