For two vertices \(u\) and \(v\) in a graph \(G\), the distance between \(u\) and \(v\), denoted by \(d(u,v)\), is the length of the shortest path between \(u\) and \(v\), if such a path exists; otherwise \(d(u,v)=\infty\). The diameter of a graph \(G\) is defined by \(\text{diam}(G)=\sup \{d(u,v) : u, v\) distinct vertices of \(G\}\). The commuting graph of a ring \({\mathcal R}\), denoted by \(\Gamma({\mathcal R})\), is a graph whose vertices are all non-central elements of \({\mathcal R}\) and two distinct vertices \(x\) and \(y\) are adjacent if and only if \(xy=yx\). Let \(D\) be a division ring and \(M_n(D)\) the set of all \(n \times n\) matrices over \(D\), \(n \geq 3\). The authors analyze the diameters of \(\Gamma(M_n(D))\) and investigate the diameters of some induced subgraphs of \(\Gamma(M_n(D))\). Specifically, they determine the diameter of the induced subgraphs on the set of non-invertible, nilpotent, idempotent and involution matrices in \(M_n(D)\). For every field \(F\), the authors show that if \(\Gamma(M_n(F))\) is a connected graph, then \(\text{diam}( \Gamma(M_n(F)))\) is at most 6 and if \(F\) is an algebraically closed field or \(n\) is a prime number and \(\Gamma(M_n(F))\) is a connected graph, then \(\text{diam}( \Gamma(M_n(F)))=4\). Finally, the authors present some applications to the structure of pairs of idempotents in \(M_n(F)\), for any field \(F\) and \(n \geq 2\).