Q6 and q7

6. You are not allowed to use determinant. (a) Let A be an n x n matrix. Suppose 2A4 - 5A2 + 7A - 31n = 0. Show that A is invertible, and find its inverse. (b) Let A, B be n x n matrices. Suppose AB + bA + aB = 0 for some real numbers a * 0 and b / 0. Show that A + aIn is invertible, and find its inverse. 7. You are not allowed to use determinant. A O (a) Let A, B be 2 x 2 matrices and M = O B Suppose A and B are invertible. Show that M-1 O B-1 (b) Let A, B, C be 2 x 2 matrices, and N = A C O B Suppose A and B are invertible. Show that N is invertible and find N-1