Manipal MET2017MathematicsMathematical Reasoning
If every element of a group G is its own inverse, then G is
Options
- Afinite
- Binfinite
- Cnot abelian
- Dabelian
Correct answer
D. abelian
Step-by-step solution
Let a and b be any element of group G . aligned & a=a⁻¹, b b⁻¹, a, b G & Now, (a b)⁻¹=a b[ a, b G a b G] & b⁻¹ a⁻¹=a b b a=a b a, b G aligned Hence, commutative law holds in group G . Therefore, G is abelian group.