Proving Jordan Canonical Form for Similarity of Matrices with Same Polynomials

[Bhatia]

I have to prove the following result:

Let A,B be two n×n matrices over the field F and A,B have the same characteristic and minimal polynomials. If no eigenvalue has algebraic multiplicity greater than 3, then A and B are similar.

I have to use the following result:

If A,B are two 3×3 nilpotent matrices, then A,B are similar if and only if they have same minimal polynomial.

Please suggest how to proceed.

 

[mathwonk]

you need to understand the relationship between these polynomials and the jordan form. do you know how to prove the result you are allowed to use? Do you realize it is a special case of your problem? and are you allowed to assume that the field contains all roots of the characteristic polynomial?