In this paper

we discuss the Von Neumann regular properties of the matrixΓn:m-ring Mm:n over a Γ-ring M. The followiug main theoremes are proved. 1. If M is a Von Neumann regular Γ-ring then Mm:n is a Von Neumannregular Γn:m-ring and the ideals of Mm:n are of the form Um:n

where U isan ideal of M. 2. An ideal Q of Mm:n is Von Neumann regular if and only if there existsa Von Neumann regular ideal P of M with Q=Pm:n. 3. If V N(M) is the maximal Von Neumann regular ideal of the Γ-ring M.then V N(Mm:n)=(V N(M))m:n.