2. Let A, B E Mnxn (F). (a) Prove that if A is similar to B, then tr A = tr B. (b) Prove that if A is similar to B, then det A = det B. (c) Prove that if A is diagonalizable over F with eigenvalues A1, . .., An possibly re- peating, then tr(A) = Alt .. . + An and det A = 1 .. . An