State the reason for the following Binary Operation *, defined on the set Z of integers, to be not commutative a*b = ab3.

Question

Philoid · Accepted Answer

Here * is a binary operator defined on the set of integers Z.

To prove * is not commutative we have to give example showing that if we replace the terms with each other result are not same.

So take –1,3 є Z

Now –1 * 3 = –27 and 3 * –1 = –3

Therefore –1 * 3 ≠ 3 * –1

So * is not commutative.

State the reason for the following Binary Operation , defined on the set Z of integers, to be not commutative ab = ab³.