Q74Section C (Part C)74 of 120

Eigenvalues — rational polynomials vanishing on the spectrum

Let $A$ be a non-zero $3\times3$ matrix with integer entries. Let $\lambda_i\in\mathbb{C}$ , $1\le i\le3$ be all the eigenvalues of $A$ (not necessarily distinct). Which of the following statements are necessarily true?

Multiple select: one or more options are correct. Select all of them, then submit — marks need the exact set.

Select every correct option, then submit.

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