aspg-24-2623-1791482665 20261008180425 American Scientific Publishing Group admin@americaspg.com American Scientific Publishing Group Journal of Neutrosophic and Fuzzy Systems JNFS 2771-6430 2771-6449 2023 7 2 Noor Edin Rabeh Baghdad University, College of Science, Baghdad, Iraq Othman Al-basheer Sudan University Of Science and Technology, Faculty Of Science, Khartoum, Sudan Sara Sawalmeh Mutah University, Faculty of Science, Mutah, Jordan Rozina Ali Cairo University, Department of Mathematics, Cairo, Egypt This paper is dedicated to study the algebraic properties and substructures that are related to the symbolic 18 and 19 plithogenic square matrices, where we present many different theorems and examples to clarify the computation of symbolic 18 and 19 plithogenic determinants, and finding 18-plithogenic and 19-plithogenic eigenvalues and eigenvectors. On the other hand, we provide algorithms for computing the inverses of symbolic 18-plithogenic and 19-plithogenic matrices with necessary and sufficient conditions for the orthogonality of those matrices. 2023 08 23 2623 https://creativecommons.org/licenses/by/4.0/ 10.54216/JNFS.070201 https://www.americaspg.com/journal/24/article/2623 https://www.americaspg.com/storage/21737387886.pdf