Question

Multiplicative identity of whole number is
(a) 1
(b) 0
(c) both 0 and 1
(d) None

Answer 1

Hint: We need to find the multiplicative identity of a whole number. The whole numbers are the basic numbers we use when counting objects.

Multiplicative identity of the whole number is a property which states that if a number is multiplied by another number, such that the product is the first number itself, then the second number is called the multiplicative identity (or identity element) of the first number.

Complete step by step solution:
First, we will list some whole numbers as a series.

Thus, we get, $0, 1, 2, 3, 4, 5......$
We will check the given options and find which of the given options is the correct multiplicative identity of a whole number. 

As we know, Multiplicative identity of a whole number is a number when multiplied with another number it will give the same result. 

Let's say we have a whole number $W$, If we multiply $W$ with a particular number $I$, it will give the result as $W$.

$\Rightarrow W \times I = W$, here $W$ is a whole number and $I$ is the multiplicative Identity of $W$.
Now, we know that the product of any number with 1 is the number itself.
The product of 0 and 1 is 0, the product of 1 and 1 is 1, the product of 2 and 1 is 2, the product of 3 and 1 is 3, etc.
Therefore, we get \[0 \times 1 = 0\], \[1 \times 1 = 1\], \[2 \times 1 = 2\], \[3 \times 1 = 3\].
Thus, we can conclude that 1 is the multiplicative identity of the whole number. So, option (A) is correct.

Note:

> We know that the product of any number with 0 is 0.

The product of 0 and 0 is 0, the product of 1 and 0 is 0, the product of 2 and 0 is 0, the product of 3 and 0 is 0, etc.

Therefore, we get \[0 \times 0 = 0\], \[1 \times 0 = 0\], \[2 \times 0 = 0\], \[3 \times 0 = 0\].

Thus, we can conclude that 0 is not the multiplicative identity of the whole number.

> The number 0 is the additive identity of whole numbers.

> The number 1 is the multiplicative identity of whole numbers.