The matrix M is given by \(\mathbf{M} = \begin{pmatrix} \frac{1}{2} & -\frac{1}{2}\sqrt{3} \\ \frac{1}{2}\sqrt{3} & \frac{1}{2} \end{pmatrix} \begin{pmatrix} 14 & 0 \\ 0 & 1 \end{pmatrix}\).

(a) The matrix M represents a sequence of two geometrical transformations in the x-y plane. Give full details of each transformation, and make clear the order in which they are applied. [4]

(b) Write \(\mathbf{M}^{-1}\) as the product of two matrices, neither of which is I. [2]

\((c) Find the equations of the invariant lines, through the origin, of the transformation represented by M. [5]\)

(d) The triangle ABC in the x-y plane is transformed by M onto triangle DEF. Given that the area of triangle DEF is 28 cm², find the area of triangle ABC. [2]