VTU 4th Sem Maths | Prove Identity & Inverse Are Unique | Module 5 – Group Theory | BCS405A

In this video, we solve an important theoretical concept from Module 5 – Group Theory, part of VTU 4th Semester Mathematics (Subject Code: BCS405A).

📌 Question:
Prove the following in group theory:
(i) The identity element in a group G is unique
(ii) The inverse of every element in a group G is unique

We use the axioms of a group (associativity, identity, inverse, and closure) to logically prove these two foundational properties. These results are frequently asked in university exams and are fundamental to understanding the structure of groups in abstract algebra.

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MODULE 5 – GROUP THEORY (BCS405A)
Prove: Identity & Inverse Are Unique in Group
Group Properties Explained!

Hey VTU students!
In this video from Module 5 – Group Theory (Subject Code: BCS405A), we’ll prove two very important facts about groups:

1️⃣ The identity element in any group is unique
2️⃣ The inverse of any element in a group is also unique

These are fundamental results based on the group axioms and are often asked in theory exams. We’ll break down the proofs clearly so you understand why these properties always hold.

Let’s get started!

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