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单词 InverseOfInverseInAGroup
释义

inverse of inverse in a group


Let (G,*) be a group.We aim to prove that (a-1)-1=a for every aG.That is, the inverse of the inverse of a group element is the element itself.

By definition a*a-1=a-1*a=e, where e is the identity in G. Reinterpreting this equation we can read it as saying that a is the inverse of a-1.

In fact, consider b=a-1, the equation can be written a*b=b*a=e and thus a is the inverse of b=a-1.

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更新时间:2025/5/5 1:05:43