A Contribution To Solve A Linear Equation With One Variable And Reverse A Matrix In 3-Cyclic Refined Neutrosophic Ring

n-cyclic refined neutrosophic rings have become the focus of scientific research and various applications in recent years. Due to the complexity and versatile uses of these structures, much research and development is still needed. There are many open problems waiting to be solved in this field. This article focuses on solving some of these problems. In particular, 3-cyclic refined neutrosophic rings are emphasized and the solution of some basic problems in this context is discussed. First, a linear equation is solved and then the inverse of 2x2 matrices is found. In order to do all these, the inverse of an element taken from this ring is used. There is a need for convenience for this. Therefore, the algorithm developed to easily find the inverse of an element in 3-cycle refined neutrosophic rings is presented.