Let a = (a) be an n x n complex matrix and let a* denote the conjugate transpose of a. which of the following statements are necessarily true ? ifa is invertib

Let A = (a) be an n x n complex matrix and let A* denote the conjugate transpose of A. Which of the following statements are necessarily true ? IfA is invertible, then tr (A" A) 0, ie., the trance of A A is non-zero. (B) If tr (A A) 0, then A is invertible If | tr(A* A) | < n?, then I a, I 1 for some i, j If tr (A A) = 0, then A is the zero matrix. (A) (C) (D)