The term
agema was clearly utilised, in Antigonid armies (as well as Seleucid), as a distinct unit for both the cavalry elite and the infantry elite. Polybius clearly makes the distinction and he has not "Romanised" the word as the Amphilolis Regulation (and its copy at Cassandreia) show:
Hatzopoulos L’organisation de l’armée macédonienne sous les
Antigonides. Problèmes anciens et documents nouveaux, 153-160, 2 I. side B, l.8-12:
Of those recruited in the agema the oldest are to be forty-five years of age, unless
some of those up to fifty years are judged to be fit to perform service in that unit. Of
the peltasts (the oldest are to be) thirty-five.
Juhel and Sekunda (The "agema" and "the other Peltasts" in the late Antigonid Army, and in the Drama / Cassandreia Conscription "diagramma"
Zeitschrift für Papyrologie und Epigraphik, ISSN 0084-5388, Nº. 170, 2009 , pags. 104-108) have recently restated the point clearly in a discussion on these regulations. These units are present in the armies of Doson and Philip V and they can hardly have adopted the term from a Roman influence yet to make its presence felt post Cynoschephalae.
As for Arrian's use, the received opinion is that the Ile Basilikoi was replaced by the term
agema as was the central noble unit of the hypaspists (the Royal hypaspists). Anabasis is not a military treatise (though some have sought to see it that way) and the technical terminology is not always correct or, more to the point, correctly used. We've noted before that the
hetairoi that took the wall at Tyre with the king were (as Arrian makes plain earlier) the hypapspists and certainly the
agema or Royal hypaspists for example.
That we have a cavalry
agema and an infantry
agema at Hydaspes is no surprise if the these units had been renamed via this term. That Arrian errs with his description of the infantry (two select foot guards and hypaspists) is no surprise given he also has Craterus commanding both the centre and the left of the phalanx line at Granicus. The easist solution is that the two taxeis of the phalanx have "dropped out" of his description. It will be these which had "precedence" on the day.