Orthogonality Graphs of Matrices Over Skew Fields

The paper is devoted to studying the orthogonality graph of the matrix ring over a skew field. It is shown that for n ≥ 3 and an arbitrary skew field D, the orthogonality graph of the ring M n (D) of n × n matrices over a skew field D is connected and has diameter 4. If n = 2, then the graph of the ring M n (D) is a disjoint union of connected components of diameters 1 and 2. As a corollary, the corresponding results on the orthogonality graphs of simple Artinian rings are obtained.