Answer
The matrix is, $ AB=\left[ \begin{array}{*{35}{r}}
0 & 2 & 2 \\
0 & 0 & 4 \\
\end{array} \right]$; reflection about the x-axis.
Work Step by Step
The matrix representing the triangle 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}}
1 & 0 \\
0 & -1 \\
\end{array} \right]$
Consider the given matrices, $\begin{align}
& AB=\left[ \begin{array}{*{35}{r}}
1 & 0 \\
0 & -1 \\
\end{array} \right]\left[ \begin{array}{*{35}{r}}
0 & 2 & 2 \\
0 & 0 & -4 \\
\end{array} \right] \\
& =\left[ \begin{array}{*{35}{r}}
0 & 2 & 2 \\
0 & 0 & 4 \\
\end{array} \right]
\end{align}$
That is, the transformed graph is a triangle with vertices $\left( 0,0 \right),\left( 2,0 \right),\left( 2,4 \right)$
Therefore, the transformed triangle will be reflection about the x-axis.
The required matrix is, $ AB=\left[ \begin{array}{*{35}{r}}
0 & 2 & 2 \\
0 & 0 & 4 \\
\end{array} \right]$ and the transformed triangle will be reflection about the x-axis.
