Matrix inversion is a fundamental operation in linear algebra which arises in various scientific problems. Many applications are cast as sparse linear systems, however, when inverted, they produce dense matrices. In some cases, only a subset of the complete inverse—referred to as selected inverse—is required. This approach is especially relevant in fields like statistical learning and nano-electronics, where the underlying sparse matrices of interest often exhibit a banded arrowhead sparsity pattern or can be efficiently permuted to one. Efficient, GPU-accelerated, implementations for the selected inversion of block tridiagonal arrowhead matrices exist within the Serinv library. Our work builds upon this foundation by extending the existing selected inversion routines to cover related sparsity patterns, such as banded arrowhead and n-block diagonal arrowhead matrices. Banded implementations only work with non-zero elements of the matrix but are challenging to implement efficiently on GPUs. To address this, we explore an n-block diagonal tiling approach. Although this method may introduce some zero elements, it allows for greater efficiency, and is well-suited for parallelization on GPUs. We rely on Python for ease of use and compatibility, alongside CuPy for efficient GPU computations. This combination enables us to deliver scalable and high-performance solutions for selected inversion tasks.