If a group G has only one element a of order 2,then show that ax=xa for all x in G.

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18. If G is a group and it has only element 18. If G is a group and it has only element 'a' whose order is 2 then ax=xa
If in a group G xa=ax, then show that xa^2=a^2x and x^2a=ax^2. If in a group G xa=ax, then show that xa^2=a^2x and x^2a=ax^2.
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If a is the only element of order 2 in a group G. Prove that a∈Z(G). If a is the only element of order 2 in a group G. Prove that a∈Z(G).
If a in G, define N(a)={x in G | ax=xa}, then N(a) is a subgroup of G . If a in G, define N(a)={x in G | ax=xa}, then N(a) is a subgroup of G .
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
15. if every non-identity element of a group has order 2 then G is abelian group 15. if every non-identity element of a group has order 2 then G is abelian group
let G be a group & x be an element of odd order in G then for any element y in G their exist y^2=x let G be a group & x be an element of odd order in G then for any element y in G their exist y^2=x