Proof that (-1)*(-1) must equal 1

If (-1)*(-1)=-1 then (2-1)*(2-1) will equal 2*2-2*1-1*2-1+-1*-1 will equal -1

But it's true that the sum (2-1) times the sum (2-1) is equal to the product (1)*(1)=1, and not -1, unless of course 1*1=-1 which it doesn't.

But if (2-1)*(2-1)=2*2-2*-1+-1*2+-1*-1 will 1 which the correct solution to product of (2-1)*(2-1)=1*1=1

Can you explain the last part to me again, like what you meant by: " if (2-1)*(2-1)=2*2-2*-1+-1*2+-1*-1 will 1 which the correct solution to product of (2-1)*(2-1)=1*1=1"? Thanks

This is clever.  You could more simply say, let (-1)*(-1) = x. 

Then, (2-1)*(2-1) = 1

2*2 - 2*1 - 1*2 + x = 1

4 - 2 - 2 + x = 1 

0 + x = 1 

x = 1

That's more clear, since when he said it he went with 2*2-2*-1+-1*2+-1*-1  which then would make the equation not true since 2*2-2*-1+-1*2+-1*-1 is 5

You must be correct since google is showing the same answer. However, bing is linking me ads about toothpastes.                   

I think he messed up since there is order of operations in that case

Remember: “Please Excuse My Dear Aunt Sally”

Yeah, except I use GEMDAS, which is the same thing

You don't even need 2.  You can prove (-1)*(-1) = 1 if you just have 0, 1 and -1. 

0 = 0

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

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

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

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

(-1)*(-1) = 1

I know that, we were talking about how the thing he gave: 2*2-2*-1+-1*2+-1*-1  would be incorrect

Plus, I already knew -1 times -1 is 1...