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