You don't have to memorize it. Decrease the multiplier by 1 at a time and watch how the result changes — the rule for how signs flip will reveal itself.
"Negative times negative is positive" isn't a rule you have to force yourself to memorize — it's simply what falls out when you follow multiplication's own pattern all the way through. Starting from 3×3=9, decrease the multiplier one at a time: 3×2=6, 3×1=3, 3×0=0 — the result drops by a steady 3 each time. Carry that same pattern forward, and it's only natural that 3×(−1)=−3 — and that's exactly why positive×negative=negative.
The same holds for (−3)×B. Start from (−3)×3=−9 and decrease B: the result climbs by a steady 3 each time, reaching (−3)×0=0, and continuing the pattern smoothly means (−3)×(−1)=3. Since division is the reverse of multiplication, applying multiplication's sign rule in reverse gives you division's sign rule too.
Fix one number with the slider and decrease the other by 1 at a time, and see for yourself how the steady pattern of increase or decrease ends up flipping the sign.