Question

State the reason for the following binary operation *, defined on the set Z of integers, to be not commutative.

a * b = ab³

Answer 1

Let a, b ∈ Z, where Z is set of integers.

Given binary operation is a ∗ b = ab³ .

Now, b ∗ a = ba³ ≠ ab³ = a ∗ b. ( \(\because\) ba³ ≠ ab³ , where a and b are arbitrary integers )

Therefore, b ∗ a ≠ a ∗ b.

Therefore, the binary operation ‘∗’ is not commutative.