Block matrix/Diagonal/Eigenvalues/Exercise

Let ${}M$ be a square matrix, which can be written as a block matrix

${}M={\begin{pmatrix}A&0\\0&B\end{pmatrix}}\,$

with square matrices ${}A$ and ${}B$. Show that a number ${}\lambda \in K$ is an eigenvalue of ${}M$ if and only if ${}\lambda$ is an eigenvalue of ${}A$ or of ${}B$.

Create a solution