Proof: Basic Properties of Homomorphisms (Identities and Inverses) | Abstract Algebra

We prove two basic properties of a homomorphism f from a group G to a group H. First, we prove the homomorphism maps the identity of G to the identity of H, that is: f(e) = e. Then we prove the homomorphism maps inverses of a to corresponding inverses in H. So, f(a^-1) = [f(a)]^-1. #abstractalgebra #grouptheory

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