This is essentially because for such small matrices the characteristic polynomial leaves very little room for variation of the minimal polynomial (and other invariant factors that
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If matrices A and B are similar, matrix B can be found by applying elementary operations on the rows of matrix A, and vice versa. Obviously, the similarity between matrices is a reflective operation. That is, if A is similar to B, B is also similar to A. Furthermore, the similarity of matrices is also symmetric. See more
Similar matrices represent the same linear operator with respect to different bases (this is the motivation for the notion of similarity), and so naturally such matrices must have
matrix A. So, both A and B are similar to A, and therefore A is similar to B. However, if two matrices have the same repeated eigenvalues they may not be distinct. For example, the zero
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