Proof: Elements that Commute Have Commutative Inverses

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Издатель Apr 3, 2021

We prove if two elements commute then their inverses commute. That is, if a and b are group elements such that ab=ba, then a^-1b^-1=b^-1a^-1. The proof follows easily from the socks and shoes property - the fact that (ab)^-1=b^-1a^-1.

What are Groups: https://www.youtube.com/watch?v=dfCNJmT0-uI
Proof of Socks and Shoes Property: https://www.youtube.com/watch?v=qcn-xE_nm2s

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