Show that the relation $(- 1) (- 1) = 1$ is a consequence of the distributive law

Question

Show that the relation $(- 1) (- 1) = 1$ is a consequence of the distributive law.

This question is the first problem from 'Number Theory for Beginners" by Andre Weil. I cannot get the point from where to begin. I tried using $1\cdot 1 = 1$ and $ 1\cdot x = x $, but couldn't get somewhere. Can you help me just with a hint? I would be willing to work up from there.

Answer 1

Try to select $a$ and $b$ so that

$$\tag 1 (-1) \, (a + b)$$

can be calculated in two ways, one using the distributiving law and the other way directly calculating the product $(-1) (c)$ where $c = a + b$.

You also want to set $a$ to the get the term/action you want.