Question

Is this set closed under multiplication
{-1, 0, 1}

Answer 1

Closed under multiplication means that any member of the set times any other member of the set (including itself) yields another member of the set.

We have the combinations,

-1 * 0 = 0

-1 * 1 = -1

-1*-1 = 1

0*0 = 0

0*1 = 0

1*1 = 1

All results are from the set, so it indeed is closed.