
The multiplicative identity for the integers is
A. 0.
B. -1.
C. 1.
D. None of these.
Answer
511.5k+ views
Hint: To solve this question, we have to know that the multiplicative identity is an identity which when used to multiply with a given element in a specified set such that the element remains unchanged, i.e. $a \times e = e \times a = a$ where e is the multiplicative identity and a is any element.
Complete step-by-step answer:
As we know that,
The multiplicative identity states that any number multiplied to its multiplicative identity gives the number itself.
We have to find the multiplicative identity for the integers.
So,
Let us say ‘e’ be the multiplicative identity of any integer ‘a’.
As according to the definition of multiplicative identity,
$a \times e = e \times a = a$ ………. (i)
Let us assume the value of a = 0, as 0 is an integer.
$0 \times e = e \times 0 = 0$
Here, we know that if we multiply any number with 0, we will get the answer 0.
So, we cannot find the multiplicative identity element with 0.
Let a = 1, putting in equation (i)
$ \Rightarrow 1 \times e = e \times 1 = 1$
This can be written as:
$ \Rightarrow 1 \times e = 1$,
Solving this, we will get
$ \Rightarrow e = 1$
Now, we will check this for negative integers.
Let a = -2, put in equation (i),
$ \Rightarrow - 2 \times e = e \times - 2 = - 2$
$ \Rightarrow - 2 \times e = - 2$
Solving this, we will get
$ \Rightarrow e = 1$
Therefore, we can say that the multiplicative identity for the integers is 1.
Hence, the correct answer is option (C).
Note:In order to solve this type of problems the key is to know the definition of multiplicative identity. It is also called the Identity property of multiplication, because the identity of the number remains the same. The identity element for multiplication operation will be always 1 and for addition operation, it will be always 0.
In the same way we solved above, even if we considered any algebraic term and applied the condition to it, we get the multiplicative identity to be 1 itself.
Complete step-by-step answer:
As we know that,
The multiplicative identity states that any number multiplied to its multiplicative identity gives the number itself.
We have to find the multiplicative identity for the integers.
So,
Let us say ‘e’ be the multiplicative identity of any integer ‘a’.
As according to the definition of multiplicative identity,
$a \times e = e \times a = a$ ………. (i)
Let us assume the value of a = 0, as 0 is an integer.
$0 \times e = e \times 0 = 0$
Here, we know that if we multiply any number with 0, we will get the answer 0.
So, we cannot find the multiplicative identity element with 0.
Let a = 1, putting in equation (i)
$ \Rightarrow 1 \times e = e \times 1 = 1$
This can be written as:
$ \Rightarrow 1 \times e = 1$,
Solving this, we will get
$ \Rightarrow e = 1$
Now, we will check this for negative integers.
Let a = -2, put in equation (i),
$ \Rightarrow - 2 \times e = e \times - 2 = - 2$
$ \Rightarrow - 2 \times e = - 2$
Solving this, we will get
$ \Rightarrow e = 1$
Therefore, we can say that the multiplicative identity for the integers is 1.
Hence, the correct answer is option (C).
Note:In order to solve this type of problems the key is to know the definition of multiplicative identity. It is also called the Identity property of multiplication, because the identity of the number remains the same. The identity element for multiplication operation will be always 1 and for addition operation, it will be always 0.
In the same way we solved above, even if we considered any algebraic term and applied the condition to it, we get the multiplicative identity to be 1 itself.
Recently Updated Pages
Master Class 12 Business Studies: Engaging Questions & Answers for Success

Master Class 12 English: Engaging Questions & Answers for Success

Master Class 12 Economics: Engaging Questions & Answers for Success

Master Class 12 Social Science: Engaging Questions & Answers for Success

Master Class 12 Maths: Engaging Questions & Answers for Success

Master Class 12 Chemistry: Engaging Questions & Answers for Success

Trending doubts
In Indian rupees 1 trillion is equal to how many c class 8 maths CBSE

How many ounces are in 500 mL class 8 maths CBSE

Name the states through which the Tropic of Cancer class 8 social science CBSE

What is the value of e infty class 8 maths CBSE

Explain land use pattern in India and why has the land class 8 social science CBSE

When people say No pun intended what does that mea class 8 english CBSE
