I realize that this is a quite simple proof. I can reason the answer but cannot prove it.
Say c is a real number and has the property Q if x <= y whenever x, y in real numbers with cx <= cy. Which real numbers have property Q?
Suppose , .
Which is property Q.
Case 2: c=0
Which is trivially property Q.
Which is only property Q if x=y, but Q is for all , so case 3 does not satisfy property Q.
Thus property Q is being non-negative.