given a question
The set of all multiples of a positive integer n with operation addition is group or not group?
I realized that in my opinion it's not a group cz if the set is on multiple positive integers, it must doesn't have inverses. For example is number $2$. The addition inverse of $2$ is $-2$ and $-2$ isn't positive integers right? But on the hint answer, it's group.
My question is, is it possible the negative numbers can be the multiples of a positive numbers? It's look like multiples of $2$ is always positive right. I have abstraction like this.
And it looks like never negative right?? Please help me.