The Inverse of Matrix Solve the Following System by the Method of Inverse Matrix

Short Answer

The inverse of matrix
$\left[\begin{array}{rrr}2 & 1 & -1 \\2 & 2 & -1 \\-1 & -1 & 1\end{array}\right] \text { is }\left[\begin{array}{rrr}1 & 0 & 1 \\-1 & 1 & 0 \\0 & 1 & 2\end{array}\right]$
Solve the following system by the method of inverse matrix.
$\begin{array}{c}2 x+y-z=2 \\2 x+2 y-z=4 \\-x-y+z=-1\end{array}$