Answer
$\left[\begin{array}{c c} 1& 0& 0&0\\ -2/5& 1/5&0&0\\ -16/15&-2/15&1/3&0\\-37/15&1/15&-2/3&1\end{array} \right]$
Work Step by Step
Using a graphing calculator (see attached picture), we get the inverse matrix:
$\left[\begin{array}{c c} 1& 0& 0&0\\ -2/5& 1/5&0&0\\ -16/15&-2/15&1/3&0\\-37/15&1/15&-2/3&1\end{array} \right]$