For opposing cars, the car that could potentially cross into the path of a vehicle does NOT have the right of way.
What if car B mistakenly has his blinker on and they intend to go straight? Car A will end up pulling in front of Car B, putting everyone at risk while getting T-boned thinking they had the RoW. Even if they legally did have the RoW, turning left through potentially oncoming traffic is risky, and even more so if you try to establish RoW in the intersection.