The matrix M represents a sequence of two transformations in the x-y plane given by a one-way stretch in the x-direction, scale factor 3, followed by a reflection in the line y = x.

(a) Find M.

(b) Give full details of the geometrical transformation in the x-y plane represented by M^-1.

The matrix N is such that MN = \(\begin{pmatrix} 1 & 2 \\ 3 & 2 \end{pmatrix}\).

(c) Find N.

\((d) Find the equations of the invariant lines, through the origin, of the transformation in the x-y plane represented by MN.\)