Let $R$ be a D24: Ring such that

(i)	$0_R$ is an D270: Additive identity in $R$

A D102: Matrix $r : I \times J \to R$ is a diagonal matrix over $R$ if and only if \begin{equation} \forall \, i \in I : \forall \, j \in J \left( i \neq j \quad \implies \quad r_{i, j} = 0_R \right) \end{equation}