Abstract Algebra/Group Theory/Homomorphism/Homomorphism Maps Inverse to Inverse

Theorem edit

Let f be a homomorphism from group G to Group K.

Let g be any element of G.

f(g-1) = [f(g)]-1

Proof edit

0.     f is a homomorphism
1.     definition of inverse in G
.
2.     homomorphism f maps identity to identity
3.     as f(g) is in K, so is its inverse [f(g)]−1
.
4.     inverse on K, eK is identity of K
5.     eK is identity of K