12. If G is a group such that x.x=e for all x∈G then G is an abelian group

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If x^2 = e for all x in G then G is an abelian group proof If x^2 = e for all x in G then G is an abelian group proof
for all "x" belongs to a group G if "x.x=e" then show G is abelian group. for all "x" belongs to a group G if "x.x=e" then show G is abelian group.
Show that every group G with identity e and such that x x e for all x G is abelian Show that every group G with identity e and such that x x e for all x G is abelian
In group G if a^2= e then G is abelian In group G if a^2= e then G is abelian
If x^2=1 for all x in G then G is abelian. If x^2=1 for all x in G then G is abelian.
Proof that G is an Abelian Group if f(a) = a^(-1) is a Homomorphism Proof that G is an Abelian Group if f(a) = a^(-1) is a Homomorphism
Abstract Algebra | If G/Z(G) is cyclic then G is abelian. Abstract Algebra | If G/Z(G) is cyclic then G is abelian.
Show that a group 𝐺 is an abelian iff (ab)^2=a^2b^2 ,for all a,b∈𝐺 Show that a group 𝐺 is an abelian iff (ab)^2=a^2b^2 ,for all a,b∈𝐺