Question

Which of the following operations is commutative in R:

(a) a*b = a²b

(b) a*b = a^b

(c) a*b = a – b + ab

(d) a * b = a + b + a²b

Answer 1

(a) ∵ a*b=a^b and b*a = b²a

∴ a*b ≠ b*a

So, operation is not commutative.

(b) ∵ a*b = ab and b*a = b^a

∴ a*b ≠ b*a

So, operation is not commutative.

(c) ∵ a*b = a – a + ab

and b*a = b – a + ba

∴ a*b* ≠ b*a

So, operation is not commutative.

(d) ∵ a*b= a + b + a²b

and : b*a = b + a + b²a

∴ a*b* ≠ b*a

So, operation is not commutative.

Hence, any of these operation is not commutative.