(a(i)) For \(B=\begin{pmatrix}k&0\\0&m\end{pmatrix}\), give full details of the transformation represented by \(B\) when \(m=1\).

(a(ii)) For \(B=\begin{pmatrix}k&0\\0&m\end{pmatrix}\), give full details of the transformation represented by \(B\) when \(m=k\).

(b) For \(A=\begin{pmatrix}0&1\\-1&1\\1&1\end{pmatrix}\), \(B=\begin{pmatrix}k&0\\0&m\end{pmatrix}\), and \(C=\begin{pmatrix}2&-1&1\\1&1&2\end{pmatrix}\), show that \(ABC\) is singular.