A Simple Group Element Inverse Proof | Abstract Algebra
We prove a simple result about inverse elements in groups while gunshots rattle off in the distance of the forest. If a and b are elements of a group G with identity e such that ab = e, then we can conclude that a=b^-1 and b=a^-1. So, if two elements combine to form the identity, we can conclude they are inverses of each other - even if we only have ab = e, we do not also need ba = e, which is what we prove in this lesson, just ab = e is enough! The proof is straightforward, and we'll show 3 different strategies for it.
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