First locate your Arma 2 Folder --> Locate the BattlEye Folder and uninstall BattlEye *Delete all remaining files in that folder.
Second locate you Arma 2 AO Folder --> Go to Expansion --> BattlEye, now you uninstall and delete all remaining files in that folder.
1. Now go back to your Arma 2 AO folder and find the folder called ''BEsetup'' click the installer and wait till its done.
2. Go to your Arma 2 folder and find the folder called ''BEsetup'' click the installer and wait till its done.
3. Now start your game, and see if its works.
Incase it doesnt, try to Right click your game in Steam (Arma 2 AO) --> Properties --> Local Files --> and click [verify integrity of game cache]
This worked for me, and I hope it will for you too, incase you had problems with it and stumbled across this topic

GL