5 The matrix \(\mathbf { M }\) is given by \(\mathbf { M } = \left( \begin{array} { r r } - \frac { 3 } { 5 } & \frac { 4 } { 5 } \\ \frac { 4 } { 5 } & \frac { 3 } { 5 } \end{array} \right)\).
- The diagram in the Printed Answer Booklet shows the unit square \(O A B C\). The image of the unit square under the transformation represented by \(\mathbf { M }\) is \(O A ^ { \prime } B ^ { \prime } C ^ { \prime }\). Draw and clearly label \(O A ^ { \prime } B ^ { \prime } C ^ { \prime }\).
- Find the equation of the line of invariant points of this transformation.
- (a) Find the determinant of \(\mathbf { M }\).
(b) Describe briefly how this value relates to the transformation represented by \(\mathbf { M }\).