to prove
Η * Η’ = Η’ * Η
Η= [a b]
[c d]
H'=[a' b']
[c' d']
All you appear to have here is two unrelated matrices, H and H'.
You cannot then prove that "H*H'= H'*H" because it is not true: matrix multiplication is not commutative.
Or did you mean that H' is the transpose of H? No, that doesn't work either. So I don't know what you are asking.