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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

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(i) `a∗b=a−b`
Check commutative is `a∗b=b∗a`
`a∗b=a−b`
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