Random Mathematics - Algebra Practice

Given $A = \begin{bmatrix} 1 & 1 & 1 \\ 2 & 3 & 2 \\ 1 & 1 & 2 \end{bmatrix}$, find $A^{-1}$. Use it to solve the following system of equations: $x+y+z=1$ $2x+3y+2z=2$ $x+y+2z=4$