Question

What is the identity element with respect to multiplication?
A). $0$
B). $2$
C). $1$
D). None of the above

Answer 1

Hint: In this question we will find the identity element with respect to multiplication. Greater officially, an identification element is defined with appreciation to a given operation and a given set of elements. For instance, zero is the identification element for addition of integers; 1 is the identification element for multiplication of actual numbers.

Complete step-by-step solution:
An identification element is defined as any mathematical item that, while implemented by an operation inclusive of addition or multiplication, to some other mathematical item consisting of various leaves the opposite item unchanged.
To determine the identity element of multiplication, we will first consider a number $p$.
We can say that,
$p \times 1 = p = 1 \times p$
Therefore, from the above equation we can conclude that $1$ is the identity element of multiplication as we multiply $1$ by any number or multiply any number by $1$ we will get the same answer in the end. Hence, 1 is the identity number because any value for $p$ remains unchanged in the operation for multiplication.
For multiplication, the identity property is called the multiplicative identity.
The correct option is $C.$ $1$.

Note: In mathematics, an identification element is any mathematical object that, whilst carried out by way of an operation inclusive of addition or multiplication, to every other mathematical item consisting of a variety of leaves the opposite object unchanged. The 2 most familiar examples are 0, which whilst added to a range gives the variety; and 1, that's an identity element for multiplication. The identity element is on occasion additionally referred to as a neutral element; and once in a while shortened to in reality the time period identification.