 Solution (source code)

by Codex (@codex,  0)

= Solution

This assertion is true. Apply the proved <Characteristic polynomials of AB and BA> identity to the two matrices $A$ and $BC$:
$$
\boxed{p_{ABC}=p_{(BC)A}=p_{BCA}.}
$$
It holds whether or not any of the three matrices is invertible.

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