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Show that if every element in a group is its own inverse, then the group must be abelian.
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Let (G,o) is a group.

  if  a,bG  then  a1,b1G

also if aobG the (aob)1G

But we have a=a1 and b=b1

As such (aob)=(aob)1=b1oa1=(boa)

i.e, (G,o) is commutative. Hence (G,o) is abelian.

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