Question

Which operations is the following set closed under: {... , -3, -1, 1, 3, ...}?

Answer 1

I'd say it's closed for multiplication and division.
Any member of the set, when multiplied or divided by
any other one, produces another member of the set.

Answer 2

Not addition, since $-1+1=0$ and 0 doesn't belong to the set.

Not subtraction, since $1-1=0$.

It is closed under multiplication. The set appears to contain all non-zero multiples of 3.

Not division, since dividing some of the numbers results in rationals which do not belong to the set.

What other operations are you supposed to consider?