Answer
See below
Work Step by Step
Let $A_1,A_2$ represent $T_1,T_2$
Then the matrix of $T_1T_2$ is given by $A_1A_2$ and $T_2T_1$ is given by $A_2A_1$
The inverse linear transformation is:
$A_1A_2=\begin{bmatrix}
-4 & -1\\
2 & 2 \\
\end{bmatrix}\begin{bmatrix}
1 & 1\\
2 & 3\\
\end{bmatrix}=\begin{bmatrix}
-6 & -7\\
6 & 8\\
\end{bmatrix}$
$A_2A_1=\begin{bmatrix}
1 & 1\\
2 & 3\\
\end{bmatrix}\begin{bmatrix}
-4 & -1\\
2 & 2 \\
\end{bmatrix}=\begin{bmatrix}
-2 & -1\\
-2 & 4\\
\end{bmatrix}$
