$($a$)$ Use a method based on augmented matrices to compute the inverse of

$M=\left[\begin{array}{ccccc}1& 1& 1& 1& 1\\ 0& 1& 2& 3& -4\\ 0& 0& 1& 3& -6\\ 0& 0& 0& 1& -4\\ 0& 0& 0& 0& 1\end{array}\right]$