What do you mean back up the key? What key?
The authorization doesn't need a back up. You just authorize or deauthorize. If an authorized computer crashes and needs to be redone this may require a new authorization. If you are at the limit then you use the option to deauthorize all and force each to reauthorize. This would make it so Apple didn't think you had too many computers authorized.
The only thing that really needs to be backed up is your actual music files. Those purchased should be backed up so you don't lose the investment. You can't download them again from Apple no matter what sad story you have. :)
The other things to back up for time saving is the library files. I mentioned these already above.
Let us know what you mean by key if this doesn't help. Also let us know how our suggestions work.
bol
