If \ast is defined on the ser R of all real numbers by  \ast :a\ast b= \sqrt{a^{2}+b^{2}}, find the identity element,if it exists in R with respect to \ast.

 

 

 

 
 
 
 
 

Answers (1)

Let e be the identity element in a relation is an element such that a\ast e= e\ast a= a
Here, a\ast e= \sqrt{a^{2}+e^{2}}
         \therefore \sqrt{a^{2}+e^{2}}= a
Squasing both sides
\Rightarrow a^{2}+e^{2}= a^{2}
\Rightarrow e^{2}= 0
\Rightarrow e= 0
\therefore so,identity element for the given relation is 0

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