If I have chords
Dm, F Maj, Am and no other melodic context is provided, I just have these three chords as an information, how do I know what key is it?
From my understanding , it can be either Am or Dm (or its relative F Maj) , because the two keys/scales are kind of similar (Am scale has an B but doesn't have A#, Dm scale has A# but doesn't have B), and I have no sharps or flats, or any other melodic context to distinguish between the scales, so what is the process behind figuring this out since it's so ambiguous, at least for my level of knowledge?
The only way I could try is to translate the progression to each of the possible keys/scales and looking at the chord functions for each of them? idk
In the key of Dm: i - III - v
In the key of F Maj: vi - I - ii
In the key of Am: iv - VI - I