If you normalize your numbers to be written with digits from -5 to +5 instead of 0 to 9 in each place, then the multiplication table is more symmetrical so you

If you normalize your numbers to be written with digits from -5 to +5 instead of 0 to 9 in each place, then the multiplication table is more symmetrical so you can memorize a table 1/4 as big and then just remember the signs of each quadrant.