9 You are given the matrix \(\mathbf { M } = \left( \begin{array} { r r } 0.8 & 0.6
0.6 & - 0.8 \end{array} \right)\).
- Calculate \(\mathbf { M } ^ { 2 }\).
You are now given that the matrix \(M\) represents a reflection in a line through the origin.
- Explain how your answer to part (i) relates to this information.
- By investigating the invariant points of the reflection, find the equation of the mirror line.
- Describe fully the transformation represented by the matrix \(\mathbf { P } = \left( \begin{array} { c c } 0.8 & - 0.6
0.6 & 0.8 \end{array} \right)\). - A composite transformation is formed by the transformation represented by \(\mathbf { P }\) followed by the transformation represented by \(\mathbf { M }\). Find the single matrix that represents this composite transformation.
- The composite transformation described in part ( \(\mathbf { v }\) ) is equivalent to a single reflection. What is the equation of the mirror line of this reflection?