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

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

Then let `e` be the identity element in R

`implies a`*`e=a=e`*`a` for all `a in R`

`implies a`*`e=a` and `e`*`a=a` for all `a in R`

`implies sqrt(a^2+e^2)=a` and `sqrt(e^2+a^2)=a` for all `a in R`

`implies a^2+e^2=a^2` and `e^2+a^2=a^2` for all `a in R`

`implies e=0`