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Let A be a set having more than one element. Let * be a binary operation on A defined by `a*b=sqrt(a^2 + b^2)` for all `a , b , in Adot` Is * commutative or associative on A?

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Let * be a binary operation on A defined by `a`*`b=sqrt(a^2 + b^2)`
We have to show `a`*`b=b`*`a`
As `a`*`b=sqrt(a^2 + b^2)`.....(1)
Then
`b`*`a=sqrt(b^2 + a^2)=sqrt(a^2 + b^2)`.......(2)
Since (1)=(2)
`a`*`b=b`*`a`
...
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