how many integers are their own multiplicative inverses?
a. 0
b. 1
c. 2
d. 3
is it 2 or 3? because it could be 1, -1, and 0
2, not 3
0 is not its own inverse. 0*0 ≠ 1
In fact, 0 has no inverse -- there is no number n such that 0*n = 1
The correct answer is b. 1.
An integer is said to have a multiplicative inverse if the product of the integer and its inverse is equal to 1.
In this case, only the integer 1 has itself as its multiplicative inverse, since 1 multiplied by 1 equals 1. The integers -1 and 0 do not have multiplicative inverses since (-1) multiplied by (-1) equals 1, and 0 multiplied by any integer is always 0. So, the correct answer is 1 integer.
To determine the number of integers that are their own multiplicative inverses, we need to understand what a multiplicative inverse is.
The multiplicative inverse of a non-zero number 'a' is a number equal to 1 divided by 'a'. In mathematical terms, if 'a' is a non-zero number, its multiplicative inverse is denoted as '1/a'.
Now, consider the answer choices given:
a. 0
b. 1
c. 2
d. 3
First, let's rule out the choices that cannot have a multiplicative inverse.
Option a: 0
Zero does not have a multiplicative inverse because any number multiplied by 0 equals 0, not 1. So, 0 cannot be its own multiplicative inverse.
Option b: 1
The multiplicative inverse of 1 is itself because 1 multiplied by 1 equals 1. So, 1 is its own multiplicative inverse.
Option c: 2
The multiplicative inverse of 2 is 1/2, which is not equal to 2. Therefore, 2 is not its own multiplicative inverse.
Option d: 3
The multiplicative inverse of 3 is 1/3, which is not equal to 3. Hence, 3 is not its own multiplicative inverse.
Therefore, the correct answer is option b: 1. Only the integer 1 is its own multiplicative inverse.
The answer would be 2.
When we think of integers, there are positive and negative integers. (Positive being 1 or greater and negative being -1 or less). However, 0 is a neutral number, not positive nor negative so 0 will be excluded.