Study on Clean Matrices in M2(Z)

Abstract

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. This chapter discusses the required and sufficient criteria for a matrix A=\(\begin{bmatrix} a & b \\ c & d \end{bmatrix} \in M_2 ({\displaystyle \mathbb {Z} })\) to be clean.