for the following statement, find either a proof (if true) or counterexample (if false) For any matrix A, If A^2 is not equal to zero, then A^3 cannot equal 0. Thanks for your help. Solution Consider A 3 = 0 A.A 2 = 0 For this to be zero either A = 0 or A 2 = 0 if A 2 not euqal to 0, then A must be 0 but A is 0, then A 2 will be zero. So for A 3 = A.A 2 = 0 to be happening, A 2 must be zero. For any matrix, If A 2 is not equal to 0, then A 3 cannot be zero Note: A need not be zero for A 2 to be zero example A=[1 1 -1 -1] A 2 = 0 .