o(ab) = o(ba) | Prove that Order of ab is equal to Order of ba

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a,b element of group G,ab=ba, then o(ab)=o(a).o(b) a,b element of group G,ab=ba, then o(ab)=o(a).o(b)
O(ab)=O(ba) for all a,b in a Finite group G. O(ab)=O(ba) for all a,b in a Finite group G.
O(ab)=O(a)*O(b) where g.c.d(O(a),O(b))=1 and ab=ba. O(ab)=O(a)*O(b) where g.c.d(O(a),O(b))=1 and ab=ba.
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If a and b are two elements of a.finite group G s.t.ab=ba and (o(a),o(b))=1 then o(ab)=o(a)o(b) If a and b are two elements of a.finite group G s.t.ab=ba and (o(a),o(b))=1 then o(ab)=o(a)o(b)
The order of ab and ba are the same in any Finite Group, Proof The order of ab and ba are the same in any Finite Group, Proof
#04 trick of abstarct algebra | If in a group G , a^5=e ,aba^-1 =b^2 , then order of b is #04 trick of abstarct algebra | If in a group G , a^5=e ,aba^-1 =b^2 , then order of b is
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