Answer
The required matrix is, $ AB=\left[ \begin{array}{*{35}{r}}
0 & 4 & 4 \\
0 & 0 & -4 \\
\end{array} \right]$, horizontal stretch by a factor of 2.
Work Step by Step
The original matrix is:
$ B=\left[ \begin{array}{*{35}{r}}
0 & 2 & 2 \\
0 & 0 & -4 \\
\end{array} \right]$
The multiplication matrix is
$ A=\left[ \begin{array}{*{35}{r}}
2 & 0 \\
0 & 1 \\
\end{array} \right]$
Consider the given matrices to find
$\begin{align}
& AB=\left[ \begin{array}{*{35}{r}}
2 & 0 \\
0 & 1 \\
\end{array} \right]\left[ \begin{array}{*{35}{r}}
0 & 2 & 2 \\
0 & 0 & -4 \\
\end{array} \right] \\
& =\left[ \begin{array}{*{35}{r}}
0 & 4 & 4 \\
0 & 0 & -4 \\
\end{array} \right]
\end{align}$
That is, the transformed graph is a triangle with vertices $\left( 0,0 \right),\left( 4,0 \right),\left( 4,-4 \right)$
Thus, the matrix $ AB=\left[ \begin{array}{*{35}{r}}
0 & 4 & 4 \\
0 & 0 & -4 \\
\end{array} \right]$ and the transformed triangle will be horizontally stretched by a factor of 2.
