I would really appreciate if anyone could help me with this problem. F is a group homomorphism from G= (E, *) to H= (F,#). If , for all x e E , x*x e ker(f). Show that for all x e E, f(x-1)=f(x) Now I don't know how I should start the proof. Also, I would like to know if I can assume that Ker(f) is equal to the identity element.