Question

Write the identity element for the binary operation * on the set R₀ of all non-zero real numbers by the rule a * b = ab/2 for all a, b ∈ R₀.

Answer 1

The given binary operation is a*b = ab/2

And from the definition of identity element e, 

a*e = a ........(i) 

We have, 

a*e = ae/2……….(ii) 

Thus from (i) & (ii) ,

ae/2 = a 

or, e/2 = 1 

∴ e = 2 

Hence the identity element for this binary operation is 2.