Please answer this matrix question without using trace? Because the student has never learned what trace is. I need to teach this to a student but I don't know how to do it exactly. I don't understand what the det(xI3-A) means exactly. It looks like f(x) equals the determinant of X times an identity matrix that's a 3 x 3 minus the A matrix. I'm really confused. Thank you so much.

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