7 The set \(M\) contains all matrices of the form \(\mathbf { X } ^ { n }\), where \(\mathbf { X } = \frac { 1 } { \sqrt { 3 } } \left( \begin{array} { r r } 2 & - 1
1 & 1 \end{array} \right)\) and \(n\) is a positive integer.
- Show that \(M\) contains exactly 12 elements.
- Deduce that \(M\), together with the operation of matrix multiplication, form a cyclic group \(G\).
- Determine all the proper subgroups of \(G\).
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