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Show that if every element in a group is its own inverse, then the group must be abelian.

Mumbai University > Computer Engineering > Sem 3 > Discrete Structures

Marks: 5 Marks

Year: Dec 2013

1 Answer
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Let a, b ∈ G.

So we have $a^{-1} = a$ and $b^{-1} = b$.

Also a • b ∈ G, therefore $a • b = (a.b)^{-1}= b^{-1} • a^{-1} = b • a$.

So we have a • b = b • a,

Hence, G is abelian.

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