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The characteristic polynomial of the
matrix
\[
\left(
\begin{array}{ccc}
a & b & c \\
d & e & f \\
g & h & i \end{array}
\right)\]
is given by the equation
\[ f(\lambda)
= \left|
\begin{array}{ccc}
\lambda - a & -b & -c \\
-d & \lambda - e & -f \\
-g & -h & \lambda - i \end{array}
\right|.\]