An inverse operator

Consider a linear operator in a vector space $\mathbb{R}^3$:

$$\mathcal{A}x = \begin{pmatrix} x_1 - x_2+2x_3 \\ x_1 + x_3 \\ -x_1-x_2+x_3 \end{pmatrix}$$where $x = (x_1, x_2, x_3)$. Find the matrix of an inverse operator $\mathcal{A}^{-1}$.

If you get, for, example, a matrix $\begin{pmatrix} 1 & 2 \\ 3 & 4 \end{pmatrix}$, in the answer write $\begin{matrix} 1 & 2 \\ 3 & 4 \end{matrix}$.