aspg-39-3025-1792222400 20261017073320 American Scientific Publishing Group admin@americaspg.com American Scientific Publishing Group Neutrosophic and Information Fusion NIF 2836-7863 2024 3 1 Noor Edin Rabeh Baghdad University, College of Science, Baghdad, Iraq 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 07 11 3025 https://creativecommons.org/licenses/by/4.0/ 10.54216/NIF.030102 https://americaspg.com/journal/39/article/3025 https://americaspg.com/storage/articles/manuscripts/01M3T18K6JYAWD9YKWR7T8GQPC.pdf