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

Short Answer

The inverse of matrix $\left[\begin{array}{lll}1 & 1 & 0 \\1 & 2 & 1 \\2 & 3 & 2\end{array}\right] \text { is }\left[\begin{array}{rrr}1 & -2 & 1 \\0 & 2 & -1 \\-1 & -1 & 1\end{array}\right]$
Solve the following system by the method of inverse matrix.
$\begin{array}{r}x+y=15 \\x+2 y+z=20 \\2 x+3 y+2 z=12\end{array}$