Similarity of Jordan cannonical forms

Question

I'm struggling with this question: Determine all possible Jordan canonical forms (up to the ordering of the Jordan blocks) for a 6 ×6 matrix A, if A has an eigenvalue 2 with algebraic multiplicity 6, and geometric multiplicity 3. Explain why the obtained Jordan canonical forms are not similar (hint: consider (J −2I)²).

I have obtained the Jordan canonical forms, however, I don't understand how can they not be similar. It seems to me that Jordan canonical forms of the same matrix always have to be similar. If A has canonical forms J₁ and J₂, then A = PJ₁P^-1 and A = SJ₂S^-1 for some matrices P and S. Therefore, PJ₁P^-1 = SJ₂S^-1 => J₁ = P^-1SJ₂S^-1P = (P^-1S)J₂(P^-1S)^-1. So, J₁ and J₂ are similar.

If you could help me understand what I'm doing wrong, I'd be very thankful!