Is it possible to find the explicit inverse of $I+AB$, where $A$ is diagonal and $B$ symmetric matrix?

Question

Question. Is it possible to find the explicit inverse of $I+AB$, where $A$ is diagonal and $B$ symmetric matrix?

$A$, $B$ are non-singular, and $I+AB$ is invertible. For $B=S-I$, where $S=[s_{ij}]=[c*sinc(c\pi(i-j))]$, $i$ and $j$ are row and column indices, $sinc(x)=sin(x)/x$, $0<c<1$

It is equivalent to find the explicit inverse of $A_0+B$ where $A_0$ is diagonal and $B$ symmetric matrix.

Thanks for any feedback.