Proof: Elements that Commute Have Commutative Inverses | Abstract Algebra

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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.

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Thanks for watching! I felt this proof was short enough to upload with the whiteboard, but in the future outside lessons will be all chalkboard. I thought the reflectiveness of the whiteboard might be an issue, but it was worse than I expected!

WrathofMath

White board much easier to read despite reflections. Thank you for that and for the video. Math in nature! How poetic! 🙂

punditgi

this was so simple and straight to the point, thank you so much!

bonezaudios

I really liked the "shoes and shocks property"

RVwithhobbies

I recall a comment from a fellow student when I was an undergrad. (Sadly, time has erased his name from my memory.) "Operators which commute usually don't anticommute."

tomkerruish

I didnt knew it was also called socks and shoes! Btw, where r u?

maheshpatel

I wish my math classes took place in a forest...also I like the whiteboard, easier to read.

davidshi

first, give channel when dead thanks bye

CrankinIt

Proof: Elements that Commute Have Commutative Inverses | Abstract Algebra

Proof: Elements that Commute Have Commutative Inverses | Abstract Algebra

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