Let R be a commutative ring with identity. Then we prove $M_n(R)=GL_n(R)$ ${cup}${$A{in}M_n(R);{mid};detA{ eq}0$ and det $A{ eq}U(R)$}${cup}Z(M-n(R))$ where U(R) denotes the set of all units of R. In particular, it will be proved that the full matrix ring $M_n(F)$ over a field F is the disjoint union of the general linear group $GL_n(F)$ of degree n over the field F and the set $Z(M_n(F))$ of all zero-divisors of $M_n(F)$. Using the result and universal mapping property we prove that $M_n(F)$ is its total ring of fractions.