1(a) For nxn matrices A, B, C and I (here I is a nxn, identity matrix), given: B= I + AB and C=A + CA. Prove: B- C=I. (8 marks) ( b) For different values of k, discuss the possible solution cases of the following linear system (i.e., under what values of k, the system has unique solution, no solution or infinitely many solutions, respectively). x1 + 2x2 + X3 = 1 2x1 + 3x2 +(k+2) x3 = 3 x1 + kx2 -2x3 = 0 (8 marks) (c) If the matrix 1 01 A= 0 20 1 0 a has an eigenvalue 0, find all the eigenvalues and eigenvectors of matrix A. (9 marks)