Prove that a homomorphism is injective or trivial Let A,B be groups, and assume that |A| = 29. Let φ:A→B be a homomorphism.
a) Prove that either φ is injective or trivial. (φ is trivial if for all a∈A φ(a) = e)
b) If |B|=80, prove that φ is trivial.
Now I know that a homomorphism is injective iff the kernel is trivial. But I can't seem to figure out how to start this question. Should I assume by contradiction that φ is not injective and not trivial and try to arrive at a contradiction? Or should I show that the kernel is trivial so φ has to be injective. 
Any hints or suggestions would be really appreciated. Thanks!

Hints:


*

*The kernel of $\phi$ is a subgroup of $A$.

*The order of a subgroup must divide the order of the group.

*The image of $\phi$ is a subgroup of $B$.

