Answer
See below
Work Step by Step
The inverse linear transformation is:
$A^{-1}=\begin{bmatrix}
1 & 1\\
2 & 3
\end{bmatrix}^{-1}=\frac{1}{\det A}\begin{bmatrix}
3 & -1\\
-2 & 1
\end{bmatrix}=\frac{1}{1}\begin{bmatrix}
3 & -1\\
-2 & 1
\end{bmatrix}=\begin{bmatrix}
3 & -1 \\
-2 & 1
\end{bmatrix}$
Hence, $T_1^{-1}(x,y)=(3x-y,-2x+y)$
