Let G be an abelian group. If H = {x ? G | x = x^-1}, that is, H consists of all the elements of G which are their own inverses, prove that H is a subgroup of G.
Added by Katherine H.
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First, we need to show that the identity element of G is in H. Since the identity element e satisfies e * e = e, it is its own inverse, and thus e ∈ H. Show more…
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