Can a integer be a reciprocal of an integer?

yes, 1 and -1.

Integers are a set of whole numbers and their opposites, including zero. For example: ..., -3, -2, -1, 0, 1, 2, 3, .... The number 7.32 is not whole, so it cannot be an integer. And 1/3 is not whole...

Negative. Sorry. No you do not. Adding a negative to a negative gives you a number that is even more negative. Picture a number line. A negative number is to the left of zero, and adding a negative...

yes

Closure of the set of integers under addition.