One Equals Minus One

Resolution
This is a falsidical paradox arising from incorrect reasoning about the nature of square roots.

There are two values of $\sqrt {-1 \times -1}$.

We have:
 * $-1 = - \sqrt {-1 \times -1}$

We also have:
 * $1 = + \sqrt {-1 \times -1}$

The two are not the same thing.