  An element $a\in R$ is provided that there exists an idempotent $e\in R$ such
that $a-e\in U(R), ae=ea$ and $eae\in J(eRe)$. In this article, we investigate
strongly rad-clean matrices over a commutative local ring. We completely
determine when a $2\times 2$ matrix over a commutative local ring is strongly
rad-clean.
