I have a banded bisymmetric matrix, say

$ A = \begin{pmatrix} a & d & f & 0 & 0 \\ d & b & e & g & 0 \\ f & e & c & e & f \\ 0 & g & e & b & d \\ 0 & 0 & f & d & a \end{pmatrix} $,

not necessarily a tridiagonal 5x5 matrix, but a general bisymmetric NxN with band K.

While I know that the inverse of a band-limited matrix is not necessarily banded, can we say something if we have the above symmetry in addition ? Like, is it banded and, if so, what is the length of band ?

If the inverse is still not necessarily band-limited, is there any additional property that could help ?