(a) Given that \(A=\begin{pmatrix}2&5\\0&-1\\6&4\end{pmatrix}\) and that \(A+O=A\),

(i) state the order of the matrix \(A\),

(ii) write down the matrix \(O\).

(b) \(B=\begin{pmatrix}1&-1\\3&2\end{pmatrix}\) and \(C=\begin{pmatrix}0.4&0.2\\-0.6&0.2\end{pmatrix}\). Find the matrix product \(BC\) and state a relationship between \(B\) and \(C\).

(c) \(D=\begin{pmatrix}a&4a\\-1&5\end{pmatrix}\), where \(a\) is a positive integer. Find \(D^{-1}\) in terms of \(a\).