(a) It is given that \(A=\begin{pmatrix}4&-1\\a&b\end{pmatrix}\), \(B=\begin{pmatrix}2&3\\-5&4\end{pmatrix}\), and \(AB=\begin{pmatrix}13&8\\18&4\end{pmatrix}\). Find the value of \(a\) and of \(b\).

(b) It is given that \(X=\begin{pmatrix}3&-5\\-4&1\end{pmatrix}\), \(Y=\begin{pmatrix}-1&2\\4&0\end{pmatrix}\), and \(XZ=Y\).

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

(ii) Hence find \(Z\).