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Selecting matrices with only certain entries

Hi all -

a slightly more general but less ambitious version of my previous (as yet unanswered) question:

I set up a matrix space M (for simplicity say over a finite field F) and I have a (finite) subset S of F. I need to do a search through the elements of M which satisfy certain algebraic constraints; however I only wish to study matrices whose entries ALL lie in S.

How please do I restrict to such matrices?

Many thanks in advance