please help me with problem 4 and 5

Safari ,XIN X14 68 A Q 8 9822: BE F47:16 ... ED umich.instructure.com FB C + M Inbox (567) - jiakai... *Homework Help -... Course Hero MATH 217 All Sect. 1 ftp.invisibleup.co.. Course Hero MATH 217 All Sect... linear algebra - Problem 4. Recall that for each integer n 2 0, the set Pn of all polynomials of degree at most n is a vector space under the usual operations of adding and scaling polynomials. For a fixed n E N, consider the differentiation function D : Pn + Pn-1 defined by D(p(x)) = p(x) for all p(x) E Pn. Prove or disprove the following: (a) D is a linear transformation. (b) D is injective. (c) D is surjective. Problem 5. Let A, B and C be 2 x 2 matrices and 0 the 2 x 2 zero matrix. Prove or disprove the following: (a) If A2 = 0 then A = 0. (b) If A # 0 and AB = AC then B = C. (c) If A is invertible and AB = AC, then B = C. (d) If A is invertible and A = A- then either A = I or A = -I (where I is the 2 x 2 identity matrix) Please note that Problems 3b and 6 on this homework set are recreational; you do not need to do them, and they will not be graded