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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)

R Ravindra Pindel

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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