So I want to show f(g1 + g2) = f(g1) + f(g2)?

I'm confused as to what exactly it is i'm adding, I would guess a generall 2x2 matrix i.e ((a b c d) + (e f g h)) Is this right? I don't understand exactly where O2 comes into it...

I know it's not an Isomorphism as it's not injective, due to a rotation of 2*pi, which means it's not bijective and thus not an isomorphism.

I'd guess that reflection on the other hand is an isomorphism as no single reflection gives itself, i.e you'd have to reflect through the same line twice.

Is this corect? Help would be appreciated mainly for the first part though.