Give full details of the geometrical transformation in the \(x - y\) plane represented by the matrix \(\left( \begin{array} { l l } 6 & 0 0 & 6 \end{array} \right)\).
Let \(\mathbf { A } = \left( \begin{array} { l l } 3 & 4 2 & 2 \end{array} \right)\).
The triangle \(D E F\) in the \(x - y\) plane is transformed by \(\mathbf { A }\) onto triangle \(P Q R\).
Given that the area of triangle \(D E F\) is \(13 \mathrm {~cm} ^ { 2 }\), find the area of triangle \(P Q R\).
Find the matrix \(\mathbf { B }\) such that \(\mathbf { A B } = \left( \begin{array} { l l } 6 & 0 0 & 6 \end{array} \right)\).
Show that the origin is the only invariant point of the transformation in the \(x - y\) plane represented by \(\mathbf { A }\).