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Which of the following is a necessary and sufficient condition for two real $3\times 3$ matrices $A$ and $B$ to be similar $($i.e., $PAP^{-1}=B$ for an invertible real $3\times 3$ matrix $P)$?

  1. They have the same characteristic polynomial
  2. They have the same minimal polynomial
  3. They have the same minimal and characteristic polynomials
  4. None of the other three conditions
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