How do I prove this statement using the axioms of integer arithmetic: If a 0, then ab

Question

How do I prove this statement using the axioms of integer arithmetic: If a < 0, b > 0, then ab < 0?

Paul M. · Accepted Answer

I think the following lines will suffice as proof:

a<0 => -a>0 by the exclusion,if a is not equal to 0 then either a>0 or -a>0

-ab >0 (because the product of 2 numbers both > 0 is > 0)

and then ab<0 for the same reason as in the first line

How do I prove this statement using the axioms of integer arithmetic: If a < 0, b > 0, then ab < 0?