How many integers are their own multiplicative inverses? a) 0 b) 1 c) 2 d) 3

C) 2



Work Shown:

Let x be some integer from the set {..., -3, -2, -1, 0, 1, 2, 3, ...}.
The multiplicative inverse of x is a number y such that x*y = 1.

Since we want x and y to be the same, this means y = x

Use substitution to go from 
x*y = 1
to 
x*x = 1
Basically I've replaced y with x

Now solve for x
x*x = 1
x^2 = 1
x = +-sqrt(1)
x = 1 or x = -1

There are 2 values of x where they are their own multiplicative inverse
1*1 = 1
(-1)*(-1) = 1