Find which of the operations given above has identity

Solution:

An identity function is a function where each element in a set B gives the image of itself as the same element i.e., g (b) = b ∀ b ∈ B. Thus, it is of the form g(x) = x and is denoted by "I". It is called an identity function

An element e ∈ Q will be the identity element for the operation * if

a * e = a = e * a,

for all a ∈ Q

a * b = ab/4

⇒ a * e = a

⇒ ae/4 = a

⇒ e = 4

Similarly, it can be checked for e * a = a, we get e = 4 is the identity

NCERT Solutions for Class 11 Maths - Chapter 1 Exercise 1.4 Question 10

Find which of the operations given above has identity.

Summary:

Here we observed that e = 4 is the identity. An identity function is a function where each element in a set B gives the image of itself as the same element i.e., g (b) = b ∀ b ∈ B