Q1.(10%) Consider two events A and B, prove that if A and B are independent, then so are .

107台大資工 (10%) Your answer will be considered correct only if all the true statements are selected. Let A be an nxn matrix. (a) If x1 and x2are the cigenvectors of A, then x1 + x2 is also an eigenvector of A. (b) If AT = -A, then A is singular. (c) If A2 = A. (A+1)n = 1 + (2n+1)A. (d) If A = AT, then A is diagonalizable.(e) If A = and B and D are invertible,then.