If A-2 bats the ball to the floor after a poor pass from A-1 and then starts dribbling, is it correct for the official to call this a double dribble?

When A-2 bats the ball to the floor after a pass and subsequently begins to dribble, this situation does not constitute a double dribble. According to basketball rules, a player is only prohibited from dribbling a second time after having already dribbled the ball, paused, and then resumed dribbling. In this case, because A-2 did not dribble after receiving the pass but instead batted the ball, which constitutes a mere act of playing the ball rather than completing a dribble, the act of dribbling that follows is permissible.

This allowance exists because the initial action of batting the ball is not classified as the player "dribbling." Therefore, A-2 is still within their rights to begin dribbling after this maneuver without penalty. Understanding this rule helps clarify many situations that occur during a game, as batters—whether intentional or incidental—do not trigger the double dribble violation as long as they do not already have established control through a dribble before that action.