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

Theorem

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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

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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
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4.     inverse on K, eK is identity of K
5.     eK is identity of K