Let `**` be the binary operation defined on `Q`. Find which of the following binary operations are commutative
(i) `a ** b=a-b, AA a,b in Q `
(ii) ` a ** b=a^(2)+b^(2), AA a,b in Q`
(iii) `a ** b=a+ab, AA a,b in Q `
(iv) `a ** b=(a-b)^(2), AA a,b in Q`

Explanation

Given that `**` be the binary operation defined on Q.
(i) `a**b=a-b, AA a,b in Q` and `b**a=b-a`
So, `a **b ne b ** a " " [ :' b-a ne a-b] `
Hence, `**` is not commutative.
(ii) ` a**b=a^(2)+b^(2)`
`b**a = b^(2) + a^(2)`
So, `**` is commutative. ` " `" [since, '+' is on rational is commutative]
(iii) `a **b=a + ab`
`b** a=b +ab`
Clearly, `a+ab ne b + ab`
So, `**` is not commutative.
(iv) `a**b = (a-b)^(2), AA a,b in Q`
`b **a =(b-a)^(2)`
` :' (a-b)^(2)=(b-a)^(2)`
Hence, `**` is commutative.