Other and better fingering for the A chord is ( I play it like this all my live already ) ringfinger 2nd fret 2nd string, index finger 2nd fret 3rd string and middle finger on the 2nd fret 4th string, this makes all the grip smaller and way lesser chance at muting unwanted strings and it makes it way easier to change to a D or E chord since you only have to move 2 fingers instead of all 3

Herman