Answer
See below
Work Step by Step
Let's reduce $A$ to the row-echelon form
$\begin{bmatrix}
1 & 0\\
0& -2
\end{bmatrix}\approx \begin{bmatrix}
1 & 0\\
0 & 1
\end{bmatrix}$
where $1..M_2(-\frac{1}{2}) $
Thus, $T(x)=Ax=M_2(-2)x$
The transformation of $R^2$ with the matrix of transformation $A$ is a product of a reflection in the x-axis followed by a linear stretch in the y direction.
