Question

State the reason for following binary operation ‘*’, defined on the set Z of integers, to be non-commutative a * b = ab³ . Also find 2 * 3.

Answer 1

Since ab³ ≠ ba³ ∀ a, b ∈ Z 

⇒ a * b ≠ b * a

Hence, ‘*’ is not commutative 

Also, 

2 * 3 = 2 × 3³ = 54