Q. 9 D5.0( 5 Votes )

# Let ∗</span

It is given that be a binary operation on the set Q of rational numbers is defined as

a b = (a – b)2

For a, b ϵ Q, we have,

a b = (a – b)2

b a = (b – a)2 = [-(a – b)]2 = (a –b)2

a * b = b * a

the operation * is commutative.

Also, We can see that (1 * 2) * 3 ≠ 1 *(2 * 3), where 1,2,3 ϵ Q

Therefore, the operation * is not associative.

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