Final Cut Pro on two Apple ID's
I have two Apple ID's, one for my personal device (cell phone/ipad) and the other for my work (company owned) Macbook. I'm wondering if I purchase Final Cut Pro under my personal Apple ID, can I install it on my work computer (under a different Apple ID?) I hope to one day own a personal Macbook where I would install the Final Cut Pro software, but don't want to purchase it twice under separate Apple ID's unnecessarily. Hopefully this question makes sense. Not looking to cheat the system...I just don't want to personally buy it for a device that I don't actually own (work computer). Thanks in advance for your help.