Let a = [ a, 1 be an nxn complex matrix and let a denote the conjugate transpose of a. which of the following statements are necessarily true? if a is invertibl

Let A = [ a, 1 be an nxn complex matrix and let A denote the conjugate transpose of A. Which of the following statements are necessarily true? If A is invertible, then tr (A A) # O,i e, the trace of A A is non zero If tr (AA) # 0, then A is invertible If tr (AA)I, then | a, 1 If tr (AA) = 0, then A is the zero matrix