A1 shoots and miss. B1 gets the defensive rebound and throws the ball upcourt for a fast break. Before the ball crosses the midcourt line, it was partially blocked by A2 but the ball still rolls across the midcourt line. A3 gets the loose ball from his own half and dribbles upcourt again.

Is this considered backcourt violation against team A considering that the ball touches A2, goes backcourt and is returned upcourt by A3.

No, it's not. Team B had team control, therefore, it can't be a BC violation on A.

For a backcourt violation to occur, you must have the following: Team A must have control in the frontcourt, Team A must be the last to touch the ball in the frontcourt, Team A must be the first to touch the ball in the backcourt.

In your situation, Team A did not have control in the frontcourt, thus no violation.

Let's make some minor corrections here.

#1 - Team A must have team control.

#2 - The ball must attain FC status.

#3 - Team A must be the last to touch the ball BEFORE it goes into the BC. (They do not have to touch it while it is in the FC.)

#4 - Team A must be the first to touch the ball AFTER it's been in the BC. (They do not have to touch it while it is in the BC.)

Thank You.