commuting matrices & polynomials 1 I need help on this problem:
Problem:
Find two 3x3 matrices, A and B that commute with each other;
and neither A is a polynomials of B nor B is a polynomial of A

A=diag(1,1,2) en B is the matrix with rows [1,1,0\0,1,0\0,0,1].
Then AB=BA, B is not polynomial in A (B is not a diagonal matrix) en A is not polynomial in B. For any polynomial p of degree <3 with P(B)=A should have the property p(1)=1 (since p([1,1\0,1])=diag(1,1), so p(x)=1+(x-1)^2) and p(1)=2.
J. Vermeer
