What if...?

Wow, great job! Your answer is correct.

In this case both balls exchange their momentum during the collision, as well. Afterwards they move with the velocity and in the direction of the other ball. If both balls looked exactly the same, we would get the impression that they have moved through each other as if they were no barrier for each other. Both, the law of the conservation of energy and of momentum are fulfilled. It's an elastic collision. The video shows this elastic collision of the two balls.