Let * be a binary operation on the set Q of rational numbers as follow

1.	Let * be a binary operation on the set Q of rational numbers as follow. Find which of the binary operations are commutative and which are associative. a*b = ab2
Answer» a ∈ Q, be Q , a * b = ab² b * a = ba² ∴ a * b≠ b * a hence not commutative. (a * b) * c = (ab²) * c = ab²c² a * (b * c) = a * (bc²) = ab²c⁴ (a * b) * c = a * (b) ∴ * is not associative.

Let * be a binary operation on the set Q of rational numbers as follow. Find which of the binary operations are commutative and which are associative. a*b = ab2

Answer»

a ∈ Q, be Q ,

a * b = ab²

b * a = ba²

∴ a * b≠ b * a

hence not commutative.

(a * b) * c = (ab²) * c = ab²c²

a * (b * c) = a * (bc²) = ab²c⁴

(a * b) * c = a * (b)

∴ * is not associative.