1. The problem statement, all variables and given/known data Say that A is a square matrix. Show that the following statements are true, or give a counter example: a) If x is in the nullspace of A, then x is in the nullspace of A2 b) If x is in the nullspace of A2, the x is in the nullspace of A. 2. Relevant equations 3. The attempt at a solution I solved part a, or maybe I didn't. I said "Ax=0 is our assumption. A2x = A*Ax = A(0) = 0 so statement a is true." However, for part b, I stated: "A2x=0 is our assumption. Let B=A2, so Bx=0 is true. A*Ax = 0 We have no way of knowing if Ax is true yet. However if we left multiply by the inverse of A, we can see that Ax=0. Therefore the statement b is true unless the determinant of A is zero, and the inverse does not exist." However, when trying any and all matrices, some with and some without a determinant equal to zero, and finding the nullspace of the matrix squared and checking it with the original matrix, it always returns a matrix of zero. Ideas? Thanks in advance.