Prove that Every Group Homorphism Maps the Identity Element to the Identity Element

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Prove that Every Group Homorphism Maps the Identity Element to the Identity Element

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So because f(xy) on the left is the binary operation in group G and f(x)f(y) on the right is the binary operation in group H, I sometimes use SQUARE for the binary operation in G and TRIANGLE for the binary operation in H. I think things would be more clear for people if you made it explicit, instead of "overloading" the multiplication operator people are familiar with in regular algebra. So I would have f (x SQUARE y) = f(x) TRIANGLE f(y).

MrCoreyTexas

Please say using the associative axiom of the group theory in the process of the right hand side's change.

shunsukenatsusawa

What subject is this from, complex analysis?

SequinBrain

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