The question asks:

Suppose that ab > 0. Show that if a < b, then 1/b < 1/a.

I know this is correct, but I don't know how to show it. I did this:

aa^-2 < ba^-2

1/a < ba^-2

(b^-2)/a < (a^-2)/b

Hoping that I could find a way to swap the inequality sign around whilst creating the fractions required. But I can't seem to do it.

Any assistance would be great!