.Hi, I can answer most questions about the Jordan Normal Form of matrices but there are a couple that I can't think how to approach:
1) (True/False) If nxn matrices A and B (over complex numbers) have the same JNF, so too do A^2 and B^2.
Two matrices have the same JNF iff they're similar, so If are the JNF's of A,B resp., then
2) (True/False) For any nxn matrices A and B (over complex numbers), AB and BA have the same JNF.
Try to find an (easy!) example s.t. but and with different minimal polynomial