aspg-21-2106-1791468682 20261008141122 American Scientific Publishing Group admin@americaspg.com American Scientific Publishing Group International Journal of Neutrosophic Science IJNS 2692-6148 2690-6805 2023 22 2 Abuobida M. A. Alfahal Deanship of the Preparatory Year, Prince Sattam bin Abdulaziz University, Alkharj, Saudi Arabia Barbara Charchekhandra Jadavpur University, Department of Mathematics, Kolkata, India Raja Abdullah Abdulfatah Deanship of the Preparatory Year, Prince Sattam bin Abdulaziz University, Alkharj, Saudi Arabia Yaser Ahmad Alhasan Deanship of the Preparatory Year, Prince Sattam bin Abdulaziz University, Alkharj, Saudi Arabia Husain Alhayek Hama University, Department of Mathematics, Hama, Syria The concept of symbolic n-plithogenic algebraic matrices as symmetric structures with n+1 symmetric classical components with the special definition of the multiplication operation. This paper is dedicated to studying the properties of symbolic 10, and 9-plithogenic real square matrices and 11, 12-plithogenic real matrices from algebraic point of view, where algorithms for computing the eigenvalues and determinants will be proved. Also, the inverse of a symbolic n-plithogenic matrix for the special values n=10, n=9, n=11, and n=12 will be presented. 2023 35 53 2106 https://creativecommons.org/licenses/by/4.0/ 10.54216/IJNS.220204 https://www.americaspg.com/journal/21/article/2106 https://www.americaspg.com/storage/91749419063.pdf