TY - JOUR AU - Sookcharoenpinyo, Benchawan PY - 2018 TI - A characterization of clean matrices in M3(Z) JF - Naresuan University Journal: Science and Technology (NUJST); Vol 26 No 1 (2018): January - March 2018 KW - clean matrix, idempotent matrix, Diophantine equation N2 -     An n x n matrix over a commutative ring with identity is clean if it is the sum of an idempotent matrix and a unit. In 2009, Rajeswari and Aziz gave necessary and sufficient criteria for a matrix in  M 3 (Z)   to be clean and discussed the involved Diophantine equations. In this paper, we extend those results to a larger set,  M 3 (Z). We characterize when a matrix    is clean. As its application, we discuss the relation between clean matrices and the existence of non-trivial solution of certain types of Diophantine equations. UR - https://www.journal.nu.ac.th/NUJST/article/view/1585