Question

The identity elements with respect to multiplication in integers is,
A.1
B.-1
C.0
D.None

Answer 1

Hint: Use definition of multiplicative identity. Multiplicative identity property with respect to multiplication in integers says that whenever a number is multiplied by the number 1, it will give that same number as a product. “1”, it is the multiplicative identity of a number. This means that any number when multiplied by 1, results in the number itself.

Complete step-by-step answer:
Identity Element: Any mathematical object that, when applied by an operation, such as addition or multiplication, to another mathematical object, such as a number, leaves the other object unchanged is called an identity element. The two most familiar examples are 0, which when added to a number gives the number, and 1, which is an identity element for multiplication.
More formally, an identity element is defined with respect to a given operation and a given set of elements. For example, 0 is the identity element for addition of integers; 1 is the identity element for multiplication of real numbers. From these examples, it is clear that the operation must involve two elements, as addition does, not a single element, as such operations as taking a power.

Given all integers,
We have to find the multiplicative identity of integers.
As we know multiplication identity elements means any element when multiplied with any number, if you get the same number then that element is called the multiplicative identity element.
Any number when multiplied by 1, results in the number itself.
Hence, 1 is the identity element with respect to multiplication.
So, the correct answer is “Option A”.

Note: Students should need to remember that Multiplicative identity property with respect to multiplication in integers says that whenever a number is multiplied by the number 1, it will give that same number. All operations do not always have an identity element. Sometimes a set does not have an identity element for some operation. For example, the set of even numbers has no identity element for multiplication, although there is an identity element for addition.