Mathematica: solving an equation over a set

[OB1]

I have a set of elements (matrices with symbolic entries and certain special properties) which I constructed in mathematica. I would like to identify the matrices in this (finite but large) set which solve a certain linear equation. I've tried to use Solve in conjunction with Assumptions but was unsuccessful. Does anyone have any advice on this?
Thanks in advance.

 

[Simon_Tyler]

Maybe Reduce[equations&&assumptions, Domain, variables] ??
Sometimes SolveAlways[] is also useful.
But unless you post some details or a similar example, it's quite hard to be sure.