GO Classes Test Series 2024 | Mock GATE | Test 13 | Question: 28

Answer 1

If $a b a b=a a b b$, then multiplying by $a^{-1}$ on the left and $b^{-1}$ on the right gives us $b a=a b$. Hence $\text{G}$ is abelian.

Abelian Group ALL definitions & variations: Abelian Group - ALL Alternative Definitions | GATE CSE 1988, 2022