Row column, shelf vector... create a Cayley table for the type of output \[\begin{array}{|c|c c c|} \hline . & R & C & S \\ \hline R & 6vR & sc & 3x3mRS \\ C & 3x3mRC & 6vC & 3x3mCS \\ S & sc & sc & 6vS \\ \hline \end{array}\]
But is it that simple... Define a left right product, forward back product and top bottom product...
First must examine the 2x2 feeatures created by the top bottom product. We treat left right as the regular product, where row-column=scalar and column-row=matrix.