In this article, the notion of modular multiplicative inverse operator (MMIO) ℐϱ : (Z/ϱZ)* → Z/ϱZ, ℐϱ (a) = a-1, where ϱ=b × d >3 with b, d ∈ N, is introduced and studied. A general method to decompose (MMIO) over group of units of the form (Z/ϱZ)* is also discussed through a new algorithmic functional version of Bezout's theorem. As a result, interesting decomposition laws for (MMIO)'s over (Z/ϱZ)* are obtained. Several numerical examples confirming the theoretical results are also reported.