Question

Statement 1: Product of two integers with same signs is always a positive integer.

Statement 2: Product of two integers with different signs is always a positive integer.

Answer 1

If both the integers are positive, then their product is positive.
For example, $(+3)\times (+3)=(+9)$

If both the integers are negative, then their product is still positive.
For example, $(-3)\times (-3)=(+9)$

But when signs are different, i.e. one integer is positive and the other one is negative, the product of the two integers will be negative.
For example, $(+3)\times (-3)=(-9)$
and $(-3)\times (+3)=(-9)$