Phi is the mapping from Z to Z_12 by for allathat is a member of Z, phi(a)=[3a]mod 12.

-Prove that phi is homomorphism

-Determine Ker(phi)

This is what I have, but don't think it is right, can someone help me Please?

Homomorphism:

phi(ab)=(ab)^12=a^12 * b^12=phi(a)phi(b)

And the Ker(phi)=<cos 120 + i sin120>

I am completely lost and dont know if I did it right!?