Question

Write the identity element for the binary operation * defined on the set R of all real numbers by the rule a * b = 3ab/7 for all a, b ∈ R.

Answer 1

The given binary operation is a*b = 3ab/7 

Let e be the identity element 

Thus, as per the definition of an identity element a*e = a 

Applying this in the relation given we have 

3xe/7= a 

Or, 3e/7 = 1 

∴ e = 7/3 

Thus, the identity element for the given binary operation is 7/3.