If * is defined on the set R of all real numbers by `a*b=sqrt(a^2+b^2)` , find the identity element in R with respect to *.

Explanation

An identity element `e` in a relation is an element such that

`a**e = e**a = 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`

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