How do I find the eigenvalues of the matrix below,

0 A 0 0 0 ...

A' 0 A 0 0 ...

0 A' 0 A 0 ...

0 0 A' 0 A ...

...

where A is a 2x2 matrix

1 k

k 1

and A' is also a 2x2 matrix

1 -k

-k 1

Do the eigenvalues of the whole matrix depend on the eigenvalues of the block matrices A and A'?