Q: I have apps purchased on an old ipad can I use them on my new ipad air with a new apple ID

I purchased a new ipad air for my wife for chirstmas.

She owns a second generation ipad

If I setup the new ipad air with a different apple ID can the old apps be installed on the new IPAD without repurchasing the apps?

sounds confusing but my real question is

If I set up the ipad using the original user and reinstall the apps can I change apple id's and still use the installed apps?