A chord inversions

A/C# and A/E are the first and second inversions of the A major. This means that the bass tone is shifting from A to C sharp or E. Both these chords are also referred to as slash chords.

A/C#

A/E

Try in a chord progression

A - A/C# - D - E
F#m - E - A/E

Theory of the A/C# and A/E chords

Both chords consist of the notes A, C#, E. The difference is that the order of notes shifts. C# is the bass note in the first inversion and E is the bass note in the second inversion.

A comparison between the main A major and the two inversions can be seen below.

Alternative fingerings

A/C# can also be played as X4222X. This fingering can be accomplished by a full barre and can be an easier way especially in conjunction this Bm which often follows A/C# in progressions. Try for example the progression D - A/C# - Bm - G and let the index finger bar the second fret without moving it in the A/C# - Bm sequence.

Alternative chord names

A/C# is identical with C#m#5.
A/E is identical with E6sus4.

Chord construction

A x - A - E - A - C# - A
A/C# x - C# - E - A - C# - A
A/E E - A - E - A - C# - A
Guitar versions of the chord

Notes in chord

A A - C# - E
A/C# C# - E - A
A/E E - A - C#
Only the order of notes differs