How do I find out which apple id's are authorized on my computer? This is an inverse of the 'which computers have I authorized'

iTunes is fussing and refused to put some 30 apps back on my phone (mac had a hard disk crash.  Restored from backup, but not clear that all the permissions are right.)  I reentered all 3 authorizations, and got 'Already authorized' for two of them.  This reduced the unloadable app count to 20.

Anyway, my wife and I between us have at least 3 apple IDs, one of which we have changed from the older 'arbitrary character string including spaces' to the 'use a valid email address' format.  

The apps in question when I open iTunes go to apps, right click an app, and type 'get info' show the old format for the third id:  "firstname lastname" Not the user@gmail.com.

On her computer the id shows up as "firstname lastname (user@gmail.com)"

I have authorized user@gmail.com and got the 'already authorized' message.

Q1.  Where I can find out which apple id's are authorized on this computer?

Note I do NOT want to find out which comptuters this id is authorized on.
Didn't find a list, but the following strategy worked.

I logged out as me, logged in as the problem id, and attempted a sync.  This time it asked me to authorize the other two id's.

Before I had clicked Store, Authorize this computer, and entered the id and password.  I would have thought these two to be equivalent.