Journal of Neutrosophic and Fuzzy Systems JNFS 2771-6449 2771-6430 10.54216/JNFS https://www.americaspg.com/journals/show/2623 2021 2021 Baghdad University, College of Science, Baghdad, Iraq Noor Noor Sudan University Of Science and Technology, Faculty Of Science, Khartoum, Sudan Othman Al Al-Basheer Mutah University, Faculty of Science, Mutah, Jordan Sara Sawalmeh Cairo University, Department of Mathematics, Cairo, Egypt Rozina Ali 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 2023 08 23 10.54216/JNFS.070201 https://www.americaspg.com/articleinfo/24/show/2623