Phi is the mapping from Z to Z_12 by for all a that 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!?