A is a 2 x 2 matrix such that A1−1=−12 and A21−1=10. The sum of the elements of A is

A1−1=−12                (1)A21−1=10                 (2)Let A be given by A=a    bc    d. The first equation givesa−b=−1                  (3)c−d=2                     (4)For the second equation,A21−1=AA1−1=A−12=10This gives−a+2b=1               (5)−c+2d=0               (6)Eqs. (3) + (5) gives b = 0 and a = -1Eqs. (4) + (6) gives d = 2 and c = 4So the sum a + b + c + d = 5.