Suppose $R$ is the linear transformation matrix for $45º$ counterclockwise rotation and $M$ is the linear transformation matrix for horizontal reflection.

1. Write the matrix associated with $R$.

   Hint (a):

   The general matrix for counterclockwise rotation is:
   $\begin{bmatrix} \cos(\theta) & -\sin(\theta)\\ \sin(\theta) & \cos(\theta) \end{bmatrix}$

2. Write the matrix associated with $M$.

   Hint (b):

   A horizontal reflection of the point $(x, y)$ results in the point $(−x, y)$ .
   $\begin{bmatrix} a & b\\ c & d \end{bmatrix} \begin{bmatrix} x\\ y \end{bmatrix} \begin{bmatrix} -x\\ y \end{bmatrix}$

3. Write the matrix for the composition of $R$ followed by $M$.

4. Is the composition of $M$ followed by $R$ the same as your result in part (c)? Explain.