Uniqueness of Identities and Inverses (Group Theory)
Channel: Andrew Misseldine
Date: 2020-09-23

In this video, we prove that in every group there is a unique identity and for each element there is a unique inverse. We use this to prove the Shoe-Socks Principle and that inversion is an involution.

This is lecture 9 (part 2/4) of the lecture series offered by Dr. Andrew Misseldine for the course Math 4220 - Abstract Algebra I at Southern Utah University. A transcript of this lecture can be found at Dr. Misseldine's website or through his Google Drive at: https://drive.google.com/file/d/1dzo_jFl7qutEFXGZ7Ay8zrf3wCAOJnMO/view

This lecture is based upon Sections 3.1 and 3.2 of Abstract Algebra: Theory and Applications (http://abstract.ups.edu/) by Tom Judson. Please post any questions you might have below in the comment field and Dr. Misseldine (or other commenters) can answer them for you. Please also subscribe for further updates.