Answer
The required matrix is, $ AB=\left[ \begin{array}{*{35}{r}}
0 & 0 & 4 \\
0 & 2 & 2 \\
\end{array} \right]$, 90° counterclockwise rotation about the origin.
Work Step by Step
The 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}}
0 & -1 \\
1 & 0 \\
\end{array} \right]$
Consider the given matrices, $\begin{align}
& AB=\left[ \begin{array}{*{35}{r}}
0 & -1 \\
1 & 0 \\
\end{array} \right]\left[ \begin{array}{*{35}{r}}
0 & 2 & 2 \\
0 & 0 & -4 \\
\end{array} \right] \\
& =\left[ \begin{array}{*{35}{r}}
0 & 0 & 4 \\
0 & 2 & 2 \\
\end{array} \right]
\end{align}$
That is, the transformed graph is a triangle with vertices $\left( 0,0 \right),\left( 0,2 \right),\left( 4,2 \right)$
Therefore, the transformed triangle will be based on a 90° counterclockwise rotation about the origin.
The matrix $ AB=\left[ \begin{array}{*{35}{r}}
0 & 0 & 4 \\
0 & 2 & 2 \\
\end{array} \right]$ and the transformed triangle will be based on a 90° counterclockwise rotation about the origin.
