Show that \(\mathbf { M }\) is non-singular.
The hexagon \(R\) is transformed to the hexagon \(S\) by the transformation represented by the matrix \(\mathbf { M }\).
Given that the area of hexagon \(R\) is 5 square units,
find the area of hexagon \(S\).
The matrix \(\mathbf { M }\) represents an enlargement, with centre \(( 0,0 )\) and scale factor \(k\), where \(k > 0\), followed by a rotation anti-clockwise through an angle \(\theta\) about \(( 0,0 )\).