8. The transformation \(T\) in the plane consists of a translation in which the point \(( x , y )\) is transformed to the point \(( x - 1 , y + 1 )\), followed by a reflection in the line \(y = x\).
- Determine the \(3 \times 3\) matrix which represents \(T\).
- Find the equation of the line of fixed points of \(T\).
- Find \(T ^ { 2 }\) and hence write down \(T ^ { - 1 }\).