>>920
(A+B)^2 = E,
(A-B)^2 = -E,
より
 A+B = [ p, 0 ]
     [ 0, r ]
ここに p=±1, r=±1,

 A-B = [ 0, q ]
     [-q, 0 ]
ここに q=±1,

よって
 A = (1/2)[ p, q ]
       [-q, r ]

 B = (1/2)[ p, -q ]
       [ q, r ]