How to disable Time Machine for an external hard drive
Solution 1:
Turn off Time Machine with the switch in System Preferences, then remove the Backups.backupdb from drive A.
Time Machine should recognise that the disk is no longer a Time Machine backup destination, but if it doesn't, delete .com.apple.timemachine.donotpresent from the root of the disk.
Solution 2:
Go to Time Machine preferences, Ctrl-click on the drive you want to disable, you get a fold out menu with the option to disable the drive.