1. Zero has no reciprocal.
Explanation: The reciprocal of a number is defined as 1 divided by that number. However, since dividing by zero is undefined in mathematics, zero does not have a reciprocal. This is a fundamental concept in arithmetic.
2. The numbers 1 and -1 are their own reciprocals.
Explanation: A number is its own reciprocal if multiplying it by itself gives 1. When you take the reciprocal of 1 (1/1), you still get 1. Similarly, for -1, (-1) * (-1) also gives 1. Thus, both 1 and -1 are unique in that they are their own reciprocals.