MATRIX SOLUTIONS FOR THE NON-LINEAR EXPONENTIAL DIOPHANTINE EQUATION$$\left(X^a+\alpha I_q\right)^m+\left(Y^b+\beta I_q\right)^n=Z^2$$$$\alpha, \beta \in Z, A, B, M, N, Q \in \mathrm{~N}, X, Y, Z \in M_q(\mathrm{~N})$$. JPJANA 2025, 65 (1), 1-20. https://doi.org/10.17654/0972555526001.