Let A be a square matrix of order n such that A2 = A. Prove that [8] (a) Every VER can be decomposed as v = v1 + v2, where v is in the nullspace of A and v2 is in the column space of A. (b) The decomposition in (i) is unique, that is, if v = v1 + x2 = vi +va, where vi, v are in the nullspace of A and v2, v's are in the column space of A, then vi = vi and v2 = vz. 1 = =