$a < 0 < b$. Which of these is always true?

Explanation

1. 01

   A negative number times a positive number is negative: $ab < 0$.

2. 02

   The others can fail: $a = -5$, $b = 1$ gives $a^{2} > b^{2}$ and $a + b < 0$; and $\frac{1}{a} < 0 < \frac{1}{b}$ always.