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Identity in Binary Operation

If * is defin...

Question

$If * is defined on the set R_{o} of all non - zero real numbers by a * b = a + b - 5, the identity element in R for the binary operation * is$

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Solution

Given that a * b = a + b - 5.
Let e be the identity element of .
Therefore, a e = e * a = a.
a * e = a + e - 5 = a
$\Rightarrow$ e = 5.

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