Neutrosophic and Information Fusion NIF 2836-7863 10.54216/NIF https://www.americaspg.com/journals/show/3025 2023 2023 Baghdad University, College of Science, Baghdad, Iraq Noor Noor The objective of this paper is to study some of the elementary algebraic properties of 4-cyclic refined neutrosophic matrices with real entries, where we study the algebraic structure of the multiplication operation and its properties such as associativity, commutativity, and the existence of algebraic multiplication inverse. Also, we illustrate many examples that explain the validity of our work. 2024 2024 07 12 10.54216/NIF.030102 https://www.americaspg.com/articleinfo/39/show/3025