wanted: location of the theorem in Hamilton's treatise 

The reference "Hamilton 1853" is insufficient. We should refer to a specific section in that treatise.

Only then will be able to definitely resolve the question whether Hamilton was dealing with matrices of quaternions or just with quaternions. From a cursory reading of the table of contents of the treatise (https://archive.org/details/lecturesonquater00hami), I think matrices appear nowhere, and the recent revert (https://en.wikipedia.org/w/index.php?title=Cayley%E2%80%93Hamilton_theorem&oldid;=646712995) is plain wrong.