Question: Prove the following three simple assertions:

1. If \(\mathrm{A}\) is similar to \(\mathrm{B}\), and \(\mathrm{B}\) is similar to \(\mathrm{C}\), then \(\mathrm{A}\) is similar to C.
2. If 2 is an eigenvalue of \(A\), then 18 is an eigenvalue of
   \[2 A^{3}-A^{2}+3 A .\]
3. If \(A\) has \(\mathrm{n}\) linearly independent eigenvectors \(u_{1}, u_{2}, \ldots, u_{n}\), then \(A\) is diagonalizable.

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