Let f be a homomorphism from group G to group K. Let eK be identity of K.
f ( g ∗ n ∗ g − 1 ) = f ( g ) ⊛ f ( n ) ⊛ f ( g − 1 ) = f ( g ) ⊛ e K ⊛ f ( g − 1 ) = f ( g ) ⊛ f ( g − 1 ) = f ( g ∗ g − 1 ) = f ( e G ) = e K {\displaystyle f(g\ast n\ast g^{-1})=f(g)\circledast f(n)\circledast f(g^{-1})=f(g)\circledast e_{K}\circledast f(g^{-1})=f(g)\circledast f(g^{-1})=f(g\ast g^{-1})=f(e_{G})=e_{K}}