What is the product of any nonzero integer and its unique reciprocal?

The product of any nonzero integer and its unique reciprocal is always 1. This is a fundamental property of multiplicative inverses in mathematics. For any integer ( n ) (where ( n ) is not zero), the reciprocal is defined as ( \frac{1}{n} ). When you multiply ( n ) by its reciprocal ( \frac{1}{n} ), the result is:

[ n \times \frac{1}{n} = 1

]

This property applies to any nonzero integer, making it universally true. Therefore, the statement holds for all integers with the condition that they are not zero.

In contrast, considering the other options: the product cannot be 0 since this would imply at least one of the factors is zero, which contradicts the premise that the integer is nonzero. Similarly, the product cannot be -1 because ( n ) and ( \frac{1}{n} ) are both consistently positive or consistently negative for nonzero integers, leading to their product being positive. Additionally, the product cannot be the integer itself, as the operation involving multiplication by the reciprocal yields 1, not the original integer. Thus, the correct assertion is