Is the product of two numbers both less than one less than one

Question

I'm bad at mathematics, and I wanted to know something.

Say there are two numbers $a$ and $b$ where $a, b \in \Bbb R$ $-1 < a < 1$ and $-1 < b < 1$ Is it necessary that $a \times b < 1$?

Edit: I was in hurry and didn't notice the big mistake I did

Answer 1

Yes, because $|ab|=|a||b|<1\cdot 1 = 1$, hence $-1<ab<1$.

Answer 2

Not necessarily: $$ (-2)\times(-2)=4. $$ It will be true if the two numbers are positive and less than one.