I now know why -1 * -1 = 1 !

I just came across this theorem in what is mathematics ?
Why is -1 * -1 = 1 and not and not -1 * -1 = -1
Here is the proof !
Law of signs is not something that can be "proved" it is created by us to preserve another law, which we know as distributive law
Consider for example
a(b+c) = ab + ac
and assume that -1 * -1 = -1
Now if we choose a = -1, b = 1 and c = -1 then according to distributive law it LHS should be
-1(1-1) = -1(0) = 0
However RHS would give
-1(1-1) = -1*1+(-1)*(-1) = -1+(-1) = -2
and hence our distributive law fails
That is the reason we use -1*-1 = 1 instead of -1.
Got it !