is an element of group . is a homomorphism from to . Prove that .
I'm told the proof is by multiplying the two terms, like this (I guess)
but still cannot see what to do.
I also have that , are the identities in and , respectively.
is an element of group . is a homomorphism from to . Prove that .
I'm told the proof is by multiplying the two terms, like this (I guess)
but still cannot see what to do.
I also have that , are the identities in and , respectively.
Oops, sorry. It is not "inverse of a homomorphism" but "homomorphism of an inverse".
That is, if ab= e1, the identity in the first group (ring, field?), then you want to show that f(a)f(b)= e2. Well, the whole point of a homomorphism is that f(ab)= f(a)f(b). What does that tell you if ab= e1?