Write the identity element for the binary operation * defined on the set R of all real numbers by the rule

$a * b = \frac{3 a b}{7} for all a, b \in R .$

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Solution

Let e be the identity element in R with respect to * such that

$a * e = a = e * a, \forall a \in R a * e = a and e * a = a, \forall a \in R Then, \frac{3 a e}{7} = a and \frac{3 e a}{7} = a, \forall a \in R e = \frac{7}{3}, \forall a \in R$

Thus, $\frac{7}{3}$ is the identity element in R with respect to *.

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Write the identity element for the binary operation * defined on the set R of all real numbers by the rule a * b=3ab7 for all a, b ∈ R.

Let e be the identity element in R with respect to * such that a * e=a=e * a,∀ a∈Ra * e=a and e * a=a,∀ a∈RThen, 3ae7=a and 3ea7=a,∀ a∈Re=73 , ∀ a∈R Thus, 73 is the identity element in R with respect to *.

Write the identity element for the binary operation * defined on the set R of all real numbers by the rule

$a * b = \frac{3 a b}{7} for all a, b \in R .$