(a) Given

\(A=\begin{pmatrix}1&2\\0&-1\end{pmatrix},\quad B=\begin{pmatrix}1&-4\\2&5\\3&1\end{pmatrix},\quad C=\begin{pmatrix}3&-2&0\end{pmatrix},\)

write down all the possible products that can be formed by multiplying two of these matrices.

(b) Given

\(X=\begin{pmatrix}2&-2\\5&3\end{pmatrix},\qquad Y=\begin{pmatrix}4&1\\2&0\end{pmatrix},\)

(i) find \(X^{-1}\),

(ii) solve the matrix equation \(XZ=Y\).