The Core Inverse of the Anti-Triangular Block Matrix over Rings

Abstract

In this paper, we investigates the core inverse of the anti-triangular block matrix $M=\left( \begin{array}{cc} A&B\\ C&0 \end{array} \right)$ over a ring. We derive new explicit representations for the core inverse of $M$ under specific conditions. In particular, the EP property of $M$ involving two identical subblocks is investigated.