Provided your carry on meets A3's maximum size and weight restrictions, then obviously you'll have no problem carrying it on board without charge.
From A3's website:
Hand baggage - Economy class
You can carry on board the plane 1 piece of hand baggage, weighing no more than 8 kg and measuring no more than 56cm in length x 45cm in height x 25cm in width.
I assume you're concerned about the additional briefcase you'll each have. I've never had a problem with taking a case plus a laptop onto A3 flights, so I can't see this will be a problem - you're dealing with a proper airline that follows IATA carry-on guidelines, not FR :-)
A3 does not have an interline agreement with AA so through checking of bags might be difficult. You also don't say if you are travelling on a single ticket - if you've purchased separately, A3 has a number of hand luggage only fares now so you may not be able to check a case without paying the charge.