Question

Show that if a>b, then b^-1>a^-1, provided that a and b have the same sign. What happens if a>0 and b<0? Prove it in a proof.

Answer 1

Start from a>b.

What happens if you divide both sides of the inequality by (ab)? (Notice that ab>0 since a and b have the same sign).

Answer 2

Same idea is a>0 and b<0 but you'll see a different result, since dividing by a negative means the inequality flips.