It IS certainly odd. The link I pasted has steps to do things like resetting the keyboard settings, which might be worth a try. But I have no relevant experience with that particular problem! 365 has worked fine for me.

Oh, one more question: You have added Office 265 to your computer -- but is it the same computer that has/had the older version on? We had a former IT guy upgrade us all here to 365 and he never removed Office 2010. This caused conflicts, some of which didn't show up right away, but after I removed the old version, things ran much more smoothly. They were mostly in selecting and opening documents, so I doubt it would cause any keyboard/command issues...