/sci/ - Science & Math

We want to calculate the result of the following:

x + (-1)*x =
= 1*x + (-1)*x = (associative property)
= (1 + (-1))*x =
= 0*x = 0

This shows us that (-1)*x = -x (that is, a number multiplied by -1 gives its additive inverse). Now that we know that the result is 0, we solve the equation of x = -1:

-1 + (-1)*(-1) = 0

But for this to be true, (-1)*(-1) must be the additive inverse of -1, hence:

(-1)*(-1) = +1