Please provide a detailed exclamation using matrices. Thank you so much.

NOIT-DOOR cosa - sin a] cos a sin a 1. Show that the inverse of matrix A = is A-1 = sin a cos a sin a cos a 2. Let A = [ay] be a 3 x 3 matrix and define f (x) = det(x13 - A) (this is called the characteristic polynomial of A). a. Expand the determinant to show that f(x) is a polynomial of degree 3. b. How is the constant term of f (x) related to detA? c. How is the coefficient of x2 related to A? d. Prove that f (A) = 0