Nib asked, and Nib — askNib's tutor — drew the answer live at a whiteboard. This is the spoken transcript; enable JavaScript to watch it drawn.
why is a negative times a negative a positive
Is it just a rule to memorize? No, it's forced. Count down: three times minus two is minus six, then minus four, minus two, zero. The answers climb by two.
Keep the pattern going. Minus one times minus two has to be plus two, then minus two times minus two is four, and minus three times minus two is six.
Here's why nothing else works. The distributive law must hold. Minus one times minus two plus two is minus one times zero, which is zero, so the first piece must be two.
Or picture it. Multiplying by minus one flips a point across zero. Flip two and you land on minus two; flip again and you're back at two.
Real life agrees. Walk left at minus two meters per second. Three seconds ago, time minus three, you stood six meters to the right: plus six.
So the whole idea fits on one board: the pattern, the distributive law and the flip all demand it. Negative times negative is positive, forced, not a trick.
A negative times a negative is positive because every other rule of arithmetic would break if it were anything else.