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Let ** be a binary opertion on the set Q...

Let `**` be a binary opertion 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 + ab`
(iv) ` a ** b = (a-b) ^(2)`
(v) `a **b = (ab)/(4)`
(vi) `a **b =ab ^(2)`
Find which of the binary opertions are commutative and which are associative.

Text Solution

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