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A binary operation * is defined on th...

A binary operation * is defined on the set `R` of all real numbers by the rule `a*b=sqrt(a^2+b^2)` for all `a ,\ b in R` . Write the identity element for * on `Rdot`

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Let `e` be the identity element in `R` with respect to *. Then, `a*e=a=e*a forall a in R`
`sqrt(a^2+e^2)=a` and `sqrt(e^2+a^2)=a forall a in R`
`a^2+e^2=a^2` and `e^2+a^2=a^2 forall a in R`
`e=0`
Hence, `0` is the identity element in `R` with respect to *.
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