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