## Characteristic Polynomial, Eigenvalues, Diagonalization Problem (Princeton University Exam)

## Problem 178

Let

\[\begin{bmatrix}

0 & 0 & 1 \\

1 &0 &0 \\

0 & 1 & 0

\end{bmatrix}.\]

**(a)** Find the characteristic polynomial and all the eigenvalues (real and complex) of $A$. Is $A$ diagonalizable over the complex numbers?

**(b)** Calculate $A^{2009}$.

(*Princeton University, Linear Algebra Exam*)

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