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## Homework Statement

Prove for each square matrix B there is a real polynomial p(x) (not the zero polynomial) so p(B)=0

## Homework Equations

Rank-nullity? dimv = r(T) + n(T)

## 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.