Answer
See below
Work Step by Step
Let's reduce $A$ to the row-echelon form
$\begin{bmatrix}
-1 & -1\\
-1 & 0
\end{bmatrix}\approx \begin{bmatrix}
-1 & -1\\
0 & 1
\end{bmatrix}\approx\begin{bmatrix}
1 & 1\\
0 & 1
\end{bmatrix}\approx \begin{bmatrix}
1 & 0\\
0 & 1
\end{bmatrix}$
where $1. A_{12}(1)\\
2.M_1 (-1) \\
3. A_{21}(1)$
Thus, $T(x)=Ax=A_{12}(1)M_1(-1)A_{21}(1)x$
The transformation of $R^2$ with the matrix of transformation $A$ is a product of a shear parallel to the x-axis followed by a linear stretch in the x direction and followed by a shear parallel to the y-axis.
