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If * is a binary operation in N defined ...

If * is a binary operation in N defined as a*b`=a^(3)+b^(3)` , then which of the following is true :
(i) * is associative as well as commutative.
(ii) * is commutative but not associative
(iii) * is associative but not commutative
(iv) * is neither associative not commutative.

A

(A) Is `**` both associative and commutative?

B

(B) Is `**` commutative but not associative?

C

(C) Is `**` associative but not commutative?

D

(D) Is `**` neither commutative nor associative?

Text Solution

Verified by Experts

The correct Answer is:
(B) Is `**` commutative but not associative?
It is given that the binary operation `∗` on `N` is defined as
`a∗b= a^3 + b^3`
Apply the given binary operation on `b∗a`.
`b∗a= b^3 + a^3`
...
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