If * is defined on the set R of all real numbers by `a*b=sqrt(a^2+b^2) – InterviewSolution

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1.	If * is defined on the set R of all real numbers by `ab=sqrt(a^2+b^2)`, find the identity element in R with respect to .
Answer» An identity element `e` in a relation is an element such that `ae = ea = a.` Here, `a**e = sqrt(a^2+e^2)` `:. sqrt(a^2+e^2) = a` Squaring both sides, `=>a^2+e^2 = a^2` `=>e^2 = 0` `=>e = 0` So, identity element for the given relation is `0`.

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