# If * is Def D the Identit Ined on the Set R of All R Y Element If Exist in R Wi Eal Number by Th Respect *: to * Solution - Mathematics

#### Question

Sum

If * is defined on the set R of all real number by *: a * b = sqrt(a^2 + b^2) find the identity element if exist in R with respect to *

#### Solution

As per the question

Let b be the identify element then

a * b = b * a = a

a * b = sqrt((a)^2 + (b)^2) = a

⇒ (a)^2 + (b)^2 = (a)^2

⇒ b = 0

Similarly,

b * a = sqrt((b)^2 + (a)^2) = a

⇒ (b)^2 + (a)^2 = (a)^2

⇒ b = 0

Therefore, 0 is the identity element.

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