What is true of it
Amaj9 is A, C♯, E, G♯ and B — 1, 3, 5, 7 and 9 counted from A.
On an instrument that cannot reach all 5, the 5 and 1 go first, in that order.
The easiest of the 1 fingering below is 2142: 4 fingers, held at the 1st fret.
None of them uses an open string, so this chord moves up the neck unchanged — the same shape 1 fret higher is the chord a semitone above.
It leaves out the 5. 4 strings cannot carry 5 notes, and the 5 is the one this chord can lose without changing what it is.
Where its notes are on the neck
The brass dots are A, the root. Everything else is a chord tone with its degree printed in it.
With a different note underneath
Amaj9/C♯
6877
Amaj9/E
9b9b
Amaj9/G♯
1102
An inversion is the same chord with a different note lowest. The name changes to a slash name because the bass is what a listener hears as the foundation.