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Complex n-tuples, Basis and Diagonalization

Let T be an element of L(C^3) [complex 3-tuples] be the operator defined by
T(z_1, z_2, z_3) = (z_2, z_3, z_1).

a) Write the matrix of T in the standard basis of C^3.

b Find all eigenvalues of T

c) Is there a basis of C^3 such that the matrix of T in that basis is diagonal? If your answer is "NO", explain why.
If your answer is "YES", write down the matrix in that basis.

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