A characterization of clean matrices in M3(Z) - Sookcharoenpinyo, Benchawan (Naresuan University Journal: Science and Technology (NUJST); Vol 26 No 1 (2018): January - March 2018, 2018)
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.
Keywords: clean matrix, idempotent matrix, Diophantine equation