Answer
See below
Work Step by Step
Let's reduce $A$ to the row-echelon form
$\begin{bmatrix}
0 & 2\\
2 & 0
\end{bmatrix}\approx \begin{bmatrix}
2 & 0\\
0 & 2
\end{bmatrix}\approx\begin{bmatrix}
1 & 0\\
0 & 2
\end{bmatrix}\approx \begin{bmatrix}
1 & 0\\
0 & 1
\end{bmatrix}$
where $1. P_{12}\\
2. M_1(\frac{1}{2})\\
3. M_2 (\frac{1}{2})$
Thus, $T(x)=Av=P_{12}M_1(2)M_2(2)x$
The transformation of $R^2$ with the matrix of transformation $A$ is a product of a linear stretch in the y-direction followed by a linear stretch in the x-direction and followed by a reflection in $y=x$
