Find two 2 x 2 matrices A such that A
2 = I.
LET A =
P,Q
R,S
SO WE HAVE
P
2+QR=1.............P
2=1 - QR...............1
PQ+QS=0..........TAKING Q AS NOT ZERO ....P=-S..................2
RP+SR=0...........TAKING R AS NOT ZERO ....P=-S.........2
RQ+S
2=1...........S
2=1-QR.......3
SO WE CAN TAKE
P=2......S=-2......Q= 0.5 AND R=-6
THAT IS THE REQD. MATRIX =
