/sci/ - Science & Math

I have no idea how I'm supposed to prove that if a is positive and b is negative then ab is negative.

POS 1 only talks about what happens when a and b are both positive

POS 2 only says if a is a real number then a is positive or 0 or -a is positive

to be honest the "very simple" proof in the upper half of the page also loses me at the sentence "but this product is equal to 1"

I don't wanna just check the solutions at the end of the book, but I'm running out of things to think. Can I get a hint?

Feels like I'm missing the way I can leap from POS 1 and POS 2 to saying something about operations that involve both a positive and a negative number.