Prove that (-1)(-1)=1

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Known operations:

  • Addition (a+b)
  • Multiplication (a*b)
    Known axioms:
  • Commutativity (a+b=b+a, a*b=b*a)
  • Associativity ((a+b)+c=a+(b+c), (a*b)*c=a*(b*c))
  • Distributivity (a*(b+c)=a*b+a*c)
  • Inverses (a-a=0, a*a^-1=1)
  • Identities (a+0=a, a*1=a)

Notes:

  • -1 does not mean negative 1, it means the additive inverse of 1. This is because negatives are not defined under our operations.
  • You can’t assume certain trivial statements such as 0*0=0, due to them not being explicitly shown in the axioms. Prove them first before proving the statement if you use them.

And with that, prove (-1)(-1)=1.

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two negatives multiplied with eachother equal a positive so (-1)(-1) = 1

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it’s friday my brain can’t understand anything in this post

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me neither cuh thats why im asking yall to do it

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Actually (-1)(-1) = fish

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this shits due on monday chop chop

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it’s a double bladed halberd actually -1-1

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I’ve figured it out
You are vetex trying to get us to fix inverse scaling for you

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I hope you’ll find your answer here.

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MODS

bro’s tryna cheat

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-1 * -1 = 1
Multiplying a negative number by another negative number equals a positive number.
Don’t make it look like negative numbers if it’s not negative numbers, and it adds up to exactly the same number as a negative number would.

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he means proof, not giving a statement

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What? That’s it. That’s how you do it.

That’s the proof, that’s the whole equation explained.

Must I summarize how multiplication works?

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image

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knowing how to do it is how to use an oven, needing proof is explaining how the oven works in detail

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Imagine -1*1 is -1, because the 1 is being multiplied by a negative, and by 1, which will reverse it into negative, and multiply the separated number by 1, which is still 1, therefore it is negative 1, because the positive 1 was revered, and otherwise the same.

Now imagine -1*-1, It’s the same situation, but you reverse it twice.

According to your explanation, that’s it.

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1 - 1 = 0
(1 - 1)^2 = 0
1 * 1 + 1(-1) + (-1)1 + (-1)(-1)
(-1) + (-1)(-1) = 0
(-1)(-1) = 1

i think u should be able to simplify 1(-1) into -1 since
consider x times its additive inverse = (-x)x
= -(xx)
= -(x^2)
bc of associativity

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we have reached the peak of math