Ononot — Let A be a 2 \times 2 matrix. Consider the 4 \times 4 block

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Eigenvalues & Eigenvectorshard

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Let $A$ be a $2 \times 2$ matrix. Consider the $4 \times 4$ block matrix $M = \begin{pmatrix} 0 & A \\ I_2 & 0 \end{pmatrix}$ . How is the characteristic polynomial of $M$ ( $p_M(\lambda)$ ) related to that of $A$ ( $p_A(\lambda)$ )?