Proving (-1)(-1) = 1

Hello guys. For today I have decided to do a little bit of math. We all know that a negative times a negative equals a positive. Yet few of us rarely know why this is so.

When I was in seventh grade, I didn’t know either. I just knew this so I could get good math grades. Until one day, one of my genius friends named Will Chen showed me how. Below is a proof of (-1)(-1) = 1, which is essentially the same as showing that a neg x neg = positive.

-1=-1    reflexive property

-1(0) =-1(0) multiplication property

-1(0) = -1(1-1)  substitution of 1-1 for 0

0= -1(1) + (-1)(-1) substitution and distributive prop

 1(1) = (-1)(-1) addition property

1 = (-1)(-1) simplification

Well, that’s all for today! Hope your winter vacations were good!


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