Discussion
Which matrix quantity is recovered by multiplying all the eigenvalues together?
Answer: C
Setting \( \lambda = 0 \) in the characteristic polynomial gives the determinant up to sign, which yields the relation:
\[ \lambda_1 \lambda_2 \cdots \lambda_n = \det A \qquad \lambda_1 + \lambda_2 + \cdots + \lambda_n = \operatorname{tr} A \]
Together the two relations check a computed spectrum in a couple of lines.
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