6 The matrices \(\mathbf { M }\) and \(\mathbf { N }\) are \(\left( \begin{array} { l l } 0 & 1
1 & 0 \end{array} \right)\) and \(\left( \begin{array} { l l } 2 & 0
0 & 1 \end{array} \right)\) respectively.
- In this question you must show detailed reasoning.
Determine whether \(\mathbf { M }\) and \(\mathbf { N }\) commute under matrix multiplication.
- Specify the transformation of the plane associated with each of the following matrices.
- M
- N
- State the significance of the result in part (a) for the transformations associated with \(\mathbf { M }\) and \(\mathbf { N }\). [1]
- Use an algebraic method to show that all lines parallel to the \(x\)-axis are invariant lines of the transformation associated with N.