6 A transformation T of the plane has associated matrix \(\mathbf { M } = \left( \begin{array} { c c } 1 & \lambda + 1
\lambda - 1 & - 1 \end{array} \right)\), where \(\lambda\) is a non-zero
constant.
- Show that T reverses orientation.
- State, in terms of \(\lambda\), the area scale factor of T .
- Show that \(\mathbf { M } ^ { 2 } - \lambda ^ { 2 } \mathbf { I } = \mathbf { 0 }\).
- Hence specify the transformation equivalent to two applications of T .
- In the case where \(\lambda = 1 , \mathrm {~T}\) is equivalent to a transformation S followed by a reflection in the \(x\)-axis.
- Determine the matrix associated with S .
- Hence describe the transformation S .