Show that if two matrices a b hnn n 3 have the same

Question

Question: (a) Show that if two matrices A, B ∈ H^n×n, n ≤ 3, have the same minimal polynomial, then they are similar.

(b) Show by example that the statement in (a) fails if n ≥ 4.

(a) Show that if two matrices A, B ∈ H^n×n, n ≤ 6, have the same minimal polynomial and the same geometric multiplicity for every eigenvalue, then they are similar.

(b) Show by example that the statement in (a) fails if n ≥ 7.