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Question
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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