1.
Suppose A is 3×33 \times 3 matrix consisting of integer entries that are chosen at random from the set {1000,999,,999,1000}\{-1000, -999, \ldots, 999, 1000\}. Let P be the probability that either A2=IA^2 = -I or A is diagonal, where I is the 3×33 \times 3 identity matrix. Then,