1. The problem statement, all variables and given/known data For any (nxn) matrix A, prove or disprove with a counter example: 1. Rank(A^2) <= rank(A) 2. Nullity(A^2) <= nullity(A) 2. Relevant equations Rank = dimension of range Nullity = dimension of null space 3. The attempt at a solution I have been trying a few examples with both nonsingular and singular matrices and in all the cases I have found that rank(a^2) = rank(a) and like wise for the nullity. But obviously isn't enough to convince me so I was looking for some help please.