PROBLEM1. Characterize up to similarity those 3 x 3 matrices A over the real numbers such that f(A) where f(x) = x(x -1)2(x - 2)3. PROBLEM3.

(b) Prove that x2y3 + x2y2 + x2y - 2xy2 + x + y3 + y2 - Y - 1 is irreffitcible in 1[x,y]. PROBLEM4. Let A be a non-zero n x n matrix over a "field F. Prove each of the following. PROBLEM 5. Let G be a group. Prove that G is finite if and only if G has only finitely many subgroups.