Why is (-1)(-1) = 1? [duplicate]

$\begingroup$

I apologize if this is too obvious, but I crave for a reasonable definition/explanation - why is

$(-1)(-1)=1$?

Something akin to the reason $a^{-1}=\frac{1}{a}$, I.e. because $a^{-1}a^1=a^{1-1=0}=1$, so we get $a^{-1}=\frac{1}{a^1}=\frac{1}{a}$ by dividing both sides by $a^1$.

That sort of stuff.

$\endgroup$ 2

1 Answer

$\begingroup$

The similar would be $0(-1)=(1+(-1))(-1)=1(-1) + (-1)(-1)=-1+???=0$

$\endgroup$