The polynomial is $-\lambda^3+3\lambda -2$
which factorizes into ($\lambda-1$)($\lambda +1$)($\lambda -2$)
A matrix A has the above characteristic polynomial, and so its eigenvalues are 1, -1, and 2.
However, another matrix B, already in diagonal form, has the same characteristic polynomial, but with eigenvalues 1,1,-2, i.e., diagonal entries 1,1,-2.
Is this possible? Or have I gone wrong in my computations?
The problem statement does ask to show that the characteristic polynomials are the same but that the matrices A and B are not similar. So, perhaps I have found exactly what I needed, but it just seems weird...