Answer
See below
Work Step by Step
Let $A_3,A_4$ represent $T_3,T_4$
Then the matrix of $T_3T_4$ is given by $A_3A_4$ and $T_4T_3$ is given by $A_4A_3$
The inverse linear transformation is:
$A_3A_4=\begin{bmatrix}
3 & 5 & 1\\
1 & 2 & 1\\
2 & 6 & 7
\end{bmatrix}\begin{bmatrix}
1 & 1 & 3\\
0 & 1 & 2\\
3 & 5 & -1
\end{bmatrix}=\begin{bmatrix}
6 & 13 & 18\\
4 & 8 & 6\\
23 & 43 & 11
\end{bmatrix}$
$A_4A_3=\begin{bmatrix}
3 & 5 & 1\\
1 & 2 & 1\\
2 & 6 & 7
\end{bmatrix}\begin{bmatrix}
1 & 1 & 3\\
0 & 1 & 2\\
3 & 5 & -1
\end{bmatrix}=\begin{bmatrix}
10 & 25 & 23\\
5 & 14 & 15\\
12 & 19 & 1
\end{bmatrix}$
