(a) Find the values of \(a\) for which the determinant of \(\begin{pmatrix}2a&1\\4a&a\end{pmatrix}\) is \(6-3a\).

(b) Let \(A=\begin{pmatrix}2&1\\3&4\end{pmatrix}\) and \(B=\begin{pmatrix}2&0\\-3&5\end{pmatrix}\).

(i) Find \(A^{-1}\).

(ii) Hence find the matrix \(C\) such that \(AC=B\).

(c) Find the \(2\times2\) matrix \(D\) such that \(4D+3I=O\), where \(I\) is the identity matrix and \(O\) is the zero matrix.