Solving $-b<-a<b$ for true values

Question

I am having trouble with the following problem:

$$-b<-a<b$$

The above equation is true for constants $a$ and $b$. Which of the following must be true:

1. $a<0$
2. $b>0$
3. $|a|<b$

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My attempt: From the inequality, we have$$-b<a<b\implies |a|<b$$So $3$ is true. However, I'm not sure how to show whether $1$ and $2$ are true or not. Any insights?

Answer 1

Since $|a| < b$, we can conclude that $b>0$.

Let $a=0$ and hence $(1)$ is false.