1. The problem statement, all variables and given/known data Prove for each square matrix B there is a real polynomial p(x) (not the zero polynomial) so p(B)=0 2. Relevant equations Rank-nullity? dimv = r(T) + n(T) 3. The attempt at a solution I've found the dimension for nxn square matrices (n²) and a basis (1 in one place and zero in the rest for each place in the matrix) but I don't really know where to go from here. Any ideas would be great :) thanks.