# Eigenvlue of block matrix related

What are the eigenvalues of following block matrix?

$\begin{bmatrix} A & A \\ A & O \end{bmatrix}$

Where $A$ is any square matrix of order $n$,eigenvalues of $A$ are $\lambda_1,\lambda_2,\lambda_3....\lambda_n$ and $O$ is zero matrix of order $n$.

This is the Kronecker product $\pmatrix{1&1\\ 1&0}\otimes A$. Hence its eigenvalues are $\lambda_i\mu_j$ with $i=1,2,\ldots,n$ and $j=1,2$, where $\mu_1,\mu_2$ are the eigenvalues of $\pmatrix{1&1\\ 1&0}$.