Some concrete examples of $M_q(2)$ points

Given $q \in C$ invertible, Kassel says that a $M_q(2)$ point of an $R$ algebra is a $m=\left(\begin{array}{cc} A & B\\ C & D \end{array}\right)\in R^{4}$ such that $A,\,B,\,C,\,D \in R$ satisfy the following relations $$CA=qAC,$$$$DB=qBD,$$$$BA=qAB,$$$$DC=qCD,$$$$BC=CB$$$$DA-qCB=AD-\left(q^{-1}\right)BC.$$ Can anybody give me a concrete example of $M_3(C)$ matrices that form such a point? If it's not possible in $M_3(C)$, every othere concrete example is weel accepted. Thanks in advance

• I guess you probably prefer non-zero $A,B,C,D$? – Casteels Jul 6 '18 at 16:55
• Indeed I prefer non trivial examples – Dac0 Jul 7 '18 at 17:21