4 The matrices \(\mathbf { A } , \mathbf { B }\) and \(\mathbf { C }\) are given by $$\mathbf { A } = \left( \begin{array} { l l l } 1 & 2 & 3
2 & 1 & 3
3 & 2 & 5 \end{array} \right) , \mathbf { B } = \left( \begin{array} { r r } 0 & - 2
- 1 & 3
0 & 0 \end{array} \right) \text { and } \mathbf { C } = \left( \begin{array} { r r r } - 2 & - 1 & 1
1 & 1 & 3 \end{array} \right)$$

1. Show that \(\mathbf { C A B } = \left( \begin{array} { r r } 3 & - 7
   - 9 & 3 \end{array} \right)\).
2. Find the equations of the invariant lines, through the origin, of the transformation in the \(x - y\) plane represented by \(\mathbf { C A B }\).
   \includegraphics[max width=\textwidth, alt={}, center]{beb9c1f1-1676-4432-a42a-c418ff9f45d8-08_2715_31_106_2016} Let \(\mathbf { M } = \left( \begin{array} { l l } 3 & 0
   0 & 1 \end{array} \right)\).
3. Give full details of the transformation represented by \(\mathbf { M }\).
4. Find the matrix \(\mathbf { N }\) such that \(\mathbf { N M } = \mathbf { C A B }\).