It is given that \(M=\begin{pmatrix}2&p\\-3&q\end{pmatrix}\), where \(p\) and \(q\) are integers.

(i) If \(\det M=13\), find an equation connecting \(p\) and \(q\).

(ii) Given also that \(M^2=\begin{pmatrix}4-3p&12\\-6-3q&-3p+q^2\end{pmatrix}\), find a second equation connecting \(p\) and \(q\).

(iii) Find the value of \(p\) and of \(q\).