Negative 1 squared

Answer 1

-1 because the exponent is not distributed to the negative sign, so -1^2=-1*1^2=-1

Answer 2

-1

Answer 3

"If we can agree that a negative number is just a positive number multiplied by -1, then we can always write the product of two different negative numbers this way:

(-a)(-b) = (-1)(a)(-1)(b) = (-1)(-1)ab

or example,

-2 * -3 = (-1)(2)(-1)(3)

= (-1)(-1)(2)(3)

= (-1)(-1) * 6

So then the real question is,

(-1)(-1) = ?

and the answer is that the following convention has been adopted:

(-1)(-1) = +1

This convention has been adopted for the simple reason that any other convention would cause something to break.

For example, if we adopted the convention that (-1)(-1) = -1, the distributive property of multiplication wouldn't work for negative numbers:

[(a)(1+a) = a(1) + (a)(a)] where a = -1

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

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

0 = -2

As Sherlock Holmes observed, "When you have excluded the impossible, whatever remains, however improbable, must be the truth."

Since everything except +1 can be excluded as impossible, it follows that, however improbable it seems, (-1)(-1) = +1. "

source: mathforum.org/dr.math/faq/faq.negxneg.html