Formc Q1) If A, B, I are square matrices of size 4x4 with tr(AB) = 6, find tr(3AB +9BA+1)-(7 MARKS) Q2) Is the matrix 2BA*+ 2AB* hermitian? (show your work).(7 MARKS) 0 1 Q3) Is A = 1 0 unitary? nilpotent? idempotent? positive semidefi- nite? (show all of your work)(8 MARKS) Q4) If A is positive semidefinite, and so A is unitarily diagonalizable, that is 0 1 A=U DU*, where U = Find A/2(7 MARKS) 1 0 Q5) Let A= Find the singular values of A.(7 MARKS) 2 0 Q6) Let A= Find || A||2 (7 MARKS) 3 5 (Choose one of the following two questions) Q7) If the eigenvalues of the square matrix A of size 2x2 are 5, 3. Answer the following (7 MARKS)