Check the commutativity and associativity of O on `Q` defined by `a\ \ b=a^2+b^2` for all `a ,\ b in Q` .

Explanation

* is defined by `a`*`b=a^2+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^2+b^2)`*`c`

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

`(a`*`b)`*`c= a^4+b^4+2a^2b^2+c^2 ldots (i)`

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