Bull. Korean Math. Soc. Published online February 22, 2021
Mao-Ting Chien and Jie Meng
Soochow University, Taiwan, Pusan National University
Abstract : We study the solvability of the Fermat's matrix equation in some classes of 2-by-2 matrices. We prove the Fermat's matrix equation has infinitely many solutions in a set of 2-by-2 positive semidefinite integral matrices, and has no nontrivial solutions in some classes including 2-by-2 symmetric rational matrices and stochastic quadratic field matrices.
Keywords : Fermat's matrix equation; commuting family of matrices; stochastic matrices.