There is no actual support of matrix groups in polymake. Our groups are usually permutation groups.
There is only some very limited functionality to convert between matrices and permutations.
If you need the full strength of matrix groups (and polyhedral geometry) you should use
Oscar, which will become a comprehensive computer algebra system of the next generation, written in Julia. While the current version 0.5.2 is far from complete, it can do very many things already.