= Solution
\b[True.] By <Jordan normal form>, the characteristic <polynomial> records the total size of the blocks for each <eigenvalue>, while the minimal <polynomial> records the largest block for each <eigenvalue>. In dimension three this determines every block partition: for algebraic multiplicity three the possibilities $3$, $2+1$, and $1+1+1$ have largest block sizes three, two, and one; multiplicities one and two are equally immediate. Thus the two <matrices> have the same Jordan form and are conjugate. This is the <characteristic and minimal polynomials determine similarity in dimension three> phenomenon.
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