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The matrix of a linear operator \(A\) in an orthonormal basis \(\{e_1, e_2,
e_3\}\) is given to be
\begin{equation}
\underline{\sf A} = \begin{pmatrix}
0 & 1 & 0 \\
0 & 0 & 1 \\
1 & 0 & 0
\end{pmatrix}
\end{equation}
Is this operator unitary? How is the basis \(\{f_1, f_2,f_3\}\)
in which the operator is diagonal related to \(\{e_1, e_2,e_3\}\)?
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