Question

What is the multiplicative identity element in the set of whole numbers?
A) $0$
B) $ - 1$
C) $1$
D) None of these

Answer 1

Hint: According to given in the question we have to determine the multiplicative identity element in the set of whole numbers but first of all we have to understand about multiplicative identity element which is explained below:
Multiplicative identity element: Multiplicative identity element is an identity that when used to multiply a given element in a specified set leaves that element unchanged as the number 1 for the real number system.

Complete step-by-step solution:
Step 1: As we know that multiplicative identity element is an identity that when used to multiply a given element in a specified set leaves that element unchanged as the number 1 for the real number system as mentioned in the solution hint. So, first of all we have to consider some whole numbers as a and b.
Step 2: Now, as mentioned in the question and we consider the whole numbers according to multiplicative identity element,
$
   \Rightarrow a \times b = a \\
   \Rightarrow b = \dfrac{a}{a} \\
   \Rightarrow b = 1
 $
Step 3: As we can see from step 2 we have obtained a multiplicative identity element is 1.
Final solution: Hence, we have identified the multiplicative identity element in the set of whole numbers is 1.

Therefore option (C) is correct.

Note: An identity element such as 1 in the group of rational numbers without zero that in a given mathematical system leaves unchanged any element by which it is multiplied.
Whole numbers: The whole numbers can be defined as the positive integers including zero. The whole number does not contain any decimal and fractional part which means that represents that entire thing without pieces.