Check the commutativity and associativity of * on `Q` defined by `a*b=(a-b)^2` for all `a ,\ b in Q` .

Explanation

* is defined by `a`*`b=(a-b)^2`
on the set `Q`

Then we have to check that * is associative and commutative or not .

Now let `a,b,c in Q`

Then

`(a`*`b)`*`c=((a-b)^2)`*`c`

`(a`*`b)`*`c= ((a^2+b^2-2ab)-c)^2`

`(a`*`b)`*`c= (a^2+b^2-2ab)(a^2+b^2-2ab)+c^2-2(a^2+b^2-2ab)c`

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