How to prove b is positive? If A * B is positive and I know that A is positive, how do I prove that B is positive? I have to prove it with just basic laws of numbers, e.g. associative property and stuff like that.
If we know that $ab&gt;0$ and that $a&gt;0$, then we can divide both sides of the inequality by $a$ to find that $b&gt;0$. Thus, $b$ is positive. Remember that dividing both sides of an inequality does not change the inequality as long as what we're dividing by is positive.
If $b$ were $0$ then $ab$ would be $0$ too, which is not positive.

If $b$ were negative, then $ab$ would be negative (since positive times negative makes negative).

The only remaining possibility is that $b$ is positive.