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There's sort of two answers to this:

1) it's totally arbitrary, as are all the rules of math.

2) think of all numbers as vectors rather than as scalars.

... Thus all positive numbers lie to the right of the origin, or at 0 degrees - negative numbers are then at 180 degrees.

... Then when you multiply two vectors you add their angles.

... and 180 + 180 = 360 (or 0) and is therefore a positive result.

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Q: Why do two negative numbers when multiplied equal one positive?
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Multiplying negative numbers?

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