please solve this problem.. Needed all subparts will be really appreciated..

5. Let's call a 2 X 2 matrix complicated if it has the form [ a b] where a and b are real numbers. bo (a) [3 pts] Show that the product of two complicated matrices is another complicated matrix. (b) [3 pts] Show that, unlike matrices in general, complicated matrices commute. That is, if A and B are complicated matrices, then A - B = B - A. (c) [4 pts] Let CM denote the set of complicated matrices and let [1' be the complex numbers. Find a map f : CM > C with the following properties: - f is one-to-one and onto, - f preserves addition: f{A+ B) = f(A) + f(B), - f preserves multiplication: f(A - B) = f(A) - f(B). Be sure to justify that your candidate map really does satisfy all the properties Hint: the matrix J = [31 [1}] is complicated. Compute its square and make an educated guess about which complex number f(J) should be