1. ## multiplication rules

This answer is obvious, but I can't formally justify why..

Show if $a,b > 0$ then $a\cdot b > 0$.

2. If you think of multiplication as areas in the plane, two positive numbers multiplied together gives a rectangle in the first (positive) quadrant.

3. What "postulates" or previous theorems do you have to work with?

If you can use "if a> 0 and b> c then ab> ac" it is easy.

If not, perhaps you have, as part of the definition of ">", the "trichotomy" postulate:
If a and b are any two numbers, then one and only one of these is true:
1) a= b
2) a> b
3) b> a

If not either of those, what definition of ">" are you using?