Answer
See below
Work Step by Step
The inverse linear transformation is:
$A^{-1}=\begin{bmatrix}
-4 & -1\\
2 & 2
\end{bmatrix}=\frac{1}{\det A}\begin{bmatrix}
2 & 1\\
-2 & -4
\end{bmatrix}=-\frac{1}{6}\begin{bmatrix}
2 & 1\\
-2 & -4
\end{bmatrix}=\begin{bmatrix}
-\frac{1}{3} & -\frac{1}{6} \\
\frac{1}{3} & \frac{2}{3}
\end{bmatrix}$
Hence, $T_1^{-1}(x,y)=(-\frac{1}{3}x-\frac{1}{6} y,\frac{1}{3}x+\frac{2}{3} y)$
