Question

The relation $a\ast b=(a-b{)}^2$ , is commutative -

• A. True
• B. False

Answer 1

The correct option is A

True

A binary operation ${}^{\ast }$ is commutative if a ${}^{\ast }$ b = b ${}^{\ast }$ a or changing the order of inputs should not change the output. We are given a $\ast$ b = (a – b)^2. Let's find b ${}^{\ast }$ a to check if it is commutative. b ${}^{\ast }$ a = (b-a)^2. This is equal to (a-b)^2, which is a ${}^{\ast }$ b. So the given binary operation given is commutative.