Proof that (-1)*(-1), or negative one times negative one, equals 1 and not -1

If b=-1

Then in the equation, (2+b)(2+b), the solution must be 1 if it is true that 1*1=1, therefore making (-1)(-1) equal to 1.

Proof

If we assume that (-1)(-1)=-1 and b=-1 then

(2+b)(2+b)=2*2+2b+2b+b^2=4+4b+b^2 were to equal -1 then (2-1)*(2-1)=1*1 would equal -1 which is false, since we know that 1*1=1 or any positive times a positive always equals a positive.

But

If (-1)(-1) were to equal 1 then for the equation (2+b)(2+b), where b=-1, then the result 2*2+2b+2b+b^2=1 equals 1 would be true.

Therefore (-1)(-1)=1 is the only correct solution!

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