Question

Multiplicative identity of the whole number is given by?
A) \[1\]
B) $0$
C) Both $0$ and \[1\]
D) None

Answer 1

Hint:
Identity is different for different sets and different binary operations. We can see the multiplicative identity such that taking a product with which number gives the number itself. Also the identity of a set if it exists is unique.

Complete step by step solution:
We are asked to find the multiplicative identity of a whole number.
Identity of a binary operation is defined such that for every $a$, if $a * e = a$, then $e$ is the identity of the operation.
Multiplicative identity is $1$ since multiplying every number by one gives the number itself.
That is, for every whole number $a$, $a \times 1 = a$.
But taking products with zero always gives zero only.
So, zero cannot be the multiplicative identity.
Therefore the answer is option A.

Additional information:
The concept of identity is defined not only for numbers but for other sets also.
For example, in matrix we have identity matrix $I$ such that for every arbitrary matrix $A$, $AI = IA = A$

Note:
Multiplicative identity is not necessary for every set. For example, there does not exist such a number for the even number set.
Like one is the multiplicative identity, zero is the additive identity since adding zero to any whole number results in the number itself.
Inverses are also defined. The inverse of binary operation is defined such that operating with what we get the identity as the result.
So multiplicative inverse of a number is its reciprocal and additive inverse is its negative.
Since, $a \times \dfrac{1}{a} = 1$ and $a + ( - a) = 0$