In this talk we use the unit-graphs and the special unit-digraphs on matrix rings to show that every n × n nonzero matrix over \(F_q\) can be written as a sum of two \(SL_n\)-matrices when n > 1. We compute the eigenvalues of these graphs in terms of Kloosterman sums and study their spectral properties; and prove that if X is a subset of \(Mat_2(F_q)\) with size \(|X| >> q^{2.5}\) , then X contains at least two matrices whose difference has determinant α for any \(α \in F_q\) . Using this result we also prove a sum-product type result: if \(A,B,C,D \subseteq F_q\) satisfy \(|A||B||C||D| = Ω(q^{0.75})\) as q → ∞, then (A − B)(C − D) equals all of \(F_q\). In particular, if A is a subset of \(F_q\) with cardinality \(|A| >> q^{0.75}\) , then the subset (A − A)(A − A) equals all of \(F_q\) . We also recover a classical result: every element in any finite ring of odd order can be written as the sum of two units.