%A Sookcharoenpinyo, Benchawan %D 2018 %T A characterization of clean matrices in M3(Z) %K clean matrix, idempotent matrix, Diophantine equation %X     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. %U https://www.journal.nu.ac.th/NUJST/article/view/1585 %J Naresuan University Journal: Science and Technology (NUJST) %0 Journal Article %P 72-77%V 26 %N 1 %@ 2539-553X %8 2018-03-05