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Let ** be a binary operation on the set ...

Let `**` be a binary operation on the set Q of rational numbers as follows:
(i) `a**b=a-b`
(ii) `a**b=a^2+b^2`
(iii) `a**b=a+a b`
(iv) `a**b=(a-b)^2`
(v) `a*b=(a b)/4`
(vi) `a**b=a b^2`.
Find which of the binary operations are commutative and which are associative.

Text Solution

Verified by Experts

The correct Answer is:
(ii),(iv),(v) are commutative
(v) is associative
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