2 problems involving the real numbers

1. If $\displaystyle a$ and $\displaystyle b$ are real numbers, and $\displaystyle a > b$ and $\displaystyle b < 0$, then which of the following inequalities must be true?

A. $\displaystyle a > 0$

B. $\displaystyle a < 0$

C. $\displaystyle a^2 > b^2$

D. $\displaystyle a^2 < b^2$

E. $\displaystyle b^2 > 0$

(Turns out it is E but not sure why)

2. What is the smallest possible value for the product of two real numbers that differ by 6? (Without using derivatives and/or max/mins)

Why is it -9??