here are a few ways to play an A chord
X02220 (the most common way)
X02225 (fingered X01114, with first finger covering second fret's notes)
577655 (fingered 134211, first finger barre on fifth fret, others form an E style chord)
X
12
11 (this is like a C chord, but first finger barres the 9th fret.)
9 (can be played much easier using just the highest four strings)
10
9
here are a few ways to play a C chord
332010 (I added the G bass, good habits die hard)
X35553 or X3555X (easier) or X35558 (near impossible with small hands)
XX5558 (easy, but seldom used, me thinks)
8
10
10 (this is same fingering as the A {577655} but up three frets)
9
8
8
here are some ways to play an E chord
022100 (just as you learned)
X76454 or XX6454 (or since it is a E chord, 006454)
X79997 or X7999X (or use your pinky on the 12th fret for a high E)
This shows how each major chord can be played using each of the three base chords, A C E. An A chord can be played using an E chord form, barred at the fifth fret.
I know some of these will never be used by most players, but you should learn them as it only takes a few days to understand how each chord shifts up and down the neck. Then you can play an A as an E (577655), a C as an A (X35553) and a E as a C (076454).
have fun
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