Yes. The product of a negative integer and a positive integer is a negative integer.
No, if a negative integer is multiplied by a positive integer, the product is negative. However, if both of the integers are either positive or negative, the product is positive.
always a negative
A negative integer multiplied by a negative integer is always a positive integer product. -x * -y = xy
The smallest positive integer is 1. 1 is the multiplicative identity; ie anything times 1 is itself. The greatest negative integer is the most positive negative integer which is -1. Therefore the product of the greatest negative integer and the smallest positive integer is the greatest negative integer which is -1.
It is positive as for example: -2*-2*-2*-2 = 16