To give the context, I've been trying to look at different ways to convince myself how $-\times - = +$
Additive inverse of $a$ is written as $-a$
As an example the additive inverse of $-3$ is written as $-(-3)$
Also $-1$ times $-3$ is written as $(-1)\times (-3)$
Both above expressions evaluate to the same quantity $3$.
I guess it is easy to see why the additive inverse of $-3$ equals $3$ simply by staring at the equation $3+(-3) = 0$
However it must be very difficult to convince oneself why the second expression $(-1)\times (-3)$ evaluates to $3$ too. Both these operations seem related. I'm trying to figure out connection/intuition behind taking additive inverses and multiplying by $-1$. Help is appreciated. Thanks!