The standard grips this chord is usually shown with.
Amaj9 is A, C#, E, G# and B — Amaj7 with the ninth stacked above it.
It sounds a maj7 with more air in it. The ninth argues with nothing here, so it works anywhere a maj7 does.
Tonic — an extended resting chord.

| A | C# | E | G# | B |
|---|---|---|---|---|
| 1 | 3 | 5 | 7 | 9 |
Also written AM9, AΔ9, Ama9 or A major 9. The same chord either way; which spelling you meet depends on who wrote the chart.
Amaj9 in 2nd inversion puts E in the bass instead of A, the 5th of the chord. The notes are the same; what changes is what the bass line does, which is most of why you would reach for it — it lets the lowest voice move by step where the root would have jumped.
2 of Amaj9’s 14 common shapes do this:xx242412-12-11-13-12-x
Play Amaj9 as a shell — root, third and seventh — and the spare string takes the #11 (D#) or the 13 (F#).
All 14 common shapes as fret numbers, lowest string first. Hover or tap one to see it drawn.
How you get to it. The turn that lands on Amaj9 is Bm7 to E7 — the ii and the V of A — and E7 shares its third and seventh with Bm7, so the hand barely moves between them.
In which keys. Every note of Amaj9 belongs to C# minor (the ♭VI), E major (the IV, the subdominant), F# minor (the ♭III) and A major (the I, the tonic).
Every note of Amaj9 is in A major and A lydian.
Change one note of Amaj9 and you have Amaj7 (drop the ninth), Amaj11 (add the eleventh), Amaj13 (add the thirteenth), AmMaj9 (the major third becomes the minor third), Aadd9 (drop the major seventh) or A69 (the major seventh becomes the sixth).
Amaj9 is a major chord — root, major third, fifth. Major chords on every root.
The common shapes and the derived voicings come from different places, and both are explained in how this site is built.
Shows each chord the way this style would voice it, and marks which of its alternatives belong to the idiom.