G is a monoid. Inv(G) = {a E G, exists b so that a b = b a = 1}(adsbygoogle = window.adsbygoogle || []).push({});

prove that Inv(G) is a group. it's pretty obvious that inv(G) is a group. a monoid is a set with a law of composition which is associative and has a unit element. so inv(G) is clearly a group, because for all a in inv(G) there is an inverse element. but how do i prove this?

i guess i have to show that for each x in inv(G), the inverse of x is also in G. but how do i do that?

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# Prove that inv(G) is a group. G is a monoid

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