Question: By considering the effect on the unit square or otherwise write down the matrices M and R which represent a reflection in the line y=x and a rotation about the origin through an agnle $\displaystyle \theta$, respectively, Find the matrix $\displaystyle M^{-1}RM$ and describe it in words. Find the matrix product $\displaystyle R^{-1}MR$ and show that $\displaystyle R^{-1}MR$ is

$\displaystyle \begin{pmatrix} sin 2\Theta & cos 2\Theta\\ cos 2\Theta & -sin 2\Theta \end{pmatrix} $

After doing this question I wanted to ask if

$\displaystyle R^{-1}MR = $$\displaystyle \begin{pmatrix} sin 2\Theta & cos 2\Theta\\ cos 2\Theta & -sin 2\Theta \end{pmatrix} $ is

generally the required matrix for a reflection in the line $\displaystyle y=-mx$

am i right in assuming that?

thanks for helping