International Journal of Neutrosophic Science IJNS 2690-6805 2692-6148 10.54216/IJNS https://www.americaspg.com/journals/show/2106 2020 2020 Deanship of the Preparatory Year, Prince Sattam bin Abdulaziz University, Alkharj, Saudi Arabia Abuobida M. A. Alfahal Jadavpur University, Department of Mathematics, Kolkata, India Barbara .. Deanship of the Preparatory Year, Prince Sattam bin Abdulaziz University, Alkharj, Saudi Arabia Raja Abdullah Abdulfatah Deanship of the Preparatory Year, Prince Sattam bin Abdulaziz University, Alkharj, Saudi Arabia Yaser Ahmad Alhasan Hama University, Department of Mathematics, Hama, Syria Husain Alhayek 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 2023 35 53 10.54216/IJNS.220204 https://www.americaspg.com/articleinfo/21/show/2106