This answer is obvious, but I can't formally justify why..
Show if $\displaystyle a,b > 0 $ then $\displaystyle a\cdot b > 0 $.
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?