Composition of transformations
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Find the matrix that corresponds to a reflection in the \(y\)-axis and then a rotation about the origin by \(90^\circ\) clockwise.
$$\begin{aligned}
&\text{Reflection in y-axis} \rightarrow\left[\begin{array}{cc}-1 & 0 \\ 0 & 1\end{array}\right]\\
&\text{Rutation}\ 90^{\circ}| \text{clockwise} \rightarrow\left[\begin{array}{c}\cos \left(-\frac{\pi}{2}\right)-\sin \left(-\frac{\pi}{2}\right) \\ \sin \left(-\frac{\pi}{2}\right)+\cos \left(-\frac{\pi}{2}\right.\end{array}\right]=\left[\begin{array}{cc}0 & 1 \\ -1 & 0\end{array}\right]\\
&M=\left[\begin{array}{cc}0 & 1 \\ -1 & 0\end{array}\right]\left[\begin{array}{cc}-1 & 0 \\ 0 & 1\end{array}\right]=\left[\begin{array}{ll}0 & 1 \\ 1 & 0\end{array}\right]
\end{aligned}$$
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