9. Left Identity = Right Identity | Left Inverse = Right Inverse | Group Theory
Автор: Mathstronauts
Загружено: 2026-01-11
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In this lecture of Group Theory (Lecture 09), we prove two fundamental theorems of groups:
✔️ Left identity is also the right identity
✔️ Left inverse is also the right inverse
These results are extremely important for:
UPSC Mathematics Optional
CSIR NET / GATE Mathematics
MSc / BSc Mathematics
Abstract Algebra exams
We assume a set with a binary operation that is associative, has a left identity, and left inverses, and then show how full group properties follow.
📌 This lecture builds a strong conceptual foundation for:
Cancellation laws
Uniqueness of identity and inverse
Structure of algebraic systems
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