Mark the correct alternative in each of the following: For the binary operation * defined on R – {1} by the rule a * b = a + b + ab for all a, b ∈ R – {1}, the inverse of a is

Question

Philoid · Accepted Answer

For Identity element a * e = a = e * a , with ‘e’ being the identity element.

Given a * b =a + b + ab

⇒ a * e =a + e + ea

=a

⇒ e=0

For Inverse element a * b = e = b * a , with ‘b’ being the inverse element ‘a’.

Given a * b =a + b + ab

Now for a = 0.1

⇒ a * b =a + b + ab

=0 ….(1)

⇒ b * a =a + b + ab

=0 ….(2)

⇒ is the required inverse element of a .

Mark the correct alternative in each of the following:For the binary operation * defined on R – {1} by the rule a * b = a + b + ab for all a, b ∈ R – {1}, the inverse of a is

Mark the correct alternative in each of the following:
For the binary operation * defined on R – {1} by the rule a * b = a + b + ab for all a, b ∈ R – {1}, the inverse of a is