Question

Which one of the following is not necessarily a property of a group?

• A. Commutativity
• B. Associativity
• C. Existence of inverse for every element
• D. Existence of identity

Hint:

All groups are associative, but not necessarily commutative. Only abelian groups require commutativity.

Answer 1

The Correct Option is A

A group must satisfy:
- Closure
- Associativity
- Identity element exists
- Inverse for each element
Commutativity is not required unless it's an abelian (commutative) group. Hence, a group need not be commutative.