(a) Give full details of the geometrical transformation in the x-y plane represented by the matrix \(\begin{pmatrix} 6 & 0 \\ 0 & 6 \end{pmatrix}\).

Let \(\mathbf{A} = \begin{pmatrix} 3 & 4 \\ 2 & 2 \end{pmatrix}\).

(b) The triangle DEF in the x-y plane is transformed by \(\mathbf{A}\) onto triangle PQR. Given that the area of triangle DEF is 13 cm², find the area of triangle PQR.

(c) Find the matrix \(\mathbf{B}\) such that \(\mathbf{AB} = \begin{pmatrix} 6 & 0 \\ 0 & 6 \end{pmatrix}\).

(d) Show that the origin is the only invariant point of the transformation in the x-y plane represented by \(\mathbf{A}\).