Why does multiplying two negative numbers equal a positive number?
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There’s two ways to show that, a logical way and a graphical way.
The logical one is basically that “negative” means “loss”. If you’re adding a negative number you’re actually subtracting, and multiplying a positive by a negative number turns a “gain” into “loss”.
Well, if you multiply negative twice, you’re “losing loss”, so you’re gaining.
For the graphical way, imagine a number line with zero on it. Left you have negatives, right you have positives. What you’re doing when you multiply by a negative is a very specific operation: you’re reflecting the number from right to left. What was positive is now negative.
Well, if you multiply by negative twice, you’re reflecting around zero twice. What was on the right is in the left, then it’s back on the right. Back to positive.
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