Double Dribble Violation off the Backboard

Q: If a player after picking up their dribble bounces the ball off the backboard and catches it back with feet on the floor and shoots the ball, is it a violation? Also, if the player catches the ball off the backboard and shoots it before their feet touch the floor, is there a violation?

A: If the player intentionally throws the ball against the backboard:

24.1.2. A dribble starts when a player, having gained control of a live ball on the playing court, throws, taps, rolls, dribbles it on the floor or deliberately throws it against the backboard and touches it again before it touches another player.  

This would be considered a double dribble.

If a player throws the ball against the backboard in an attempt for a shot, he may rebound as normal with no penalty and may shoot either before his feet contact the floor or after.