Hey I've been working on this question,

How that the following is a homomorphism

From what it looks like it isn't a homomorphism but I'm not sure how to evaluate the last line,

It would be easy if the group commuted..

Does anyone know how to evaluate it?

I also have another question which I solved numerically but I'm not sure how to show it algebraically,

Would anyone know how to show

Or would it be sufficient to just know that its not true?