  Following O'Meara's result [Journal of Algebra and Its Applications
Vol~\textbf{13}, No. 8 (2014)], it follows that the block matrix
  $A=\begin{pmatrix}
  B & 0
  0 & 0
  \end{pmatrix} \in M_{n+r}(R)$, $B\in M_n(R)$, $r\ge 1$,
  over a von Neumann regular separative ring $R$, is a product of idempotent
matrices. Furthermore, this decomposition into idempotents of $A$ also holds
when $B$ is an invertible matrix and $R$ is a GE ring (defined by Cohn [New
mathematical monographs: {\bf 3}, Cambridge University Press (2006)]). As a
consequence, it follows that if there exists an example of a von Neumann
regular ring $R$ over which the matrix
  $
  A=\begin{pmatrix}
  B & 0
  0 & 0
  \end{pmatrix} \in M_{n+r}(R)
  $
  where $B\in M_n(R)$, $r\ge 1$ , cannot be expressed as a product of
idempotents, then $R$ is not separative, thus providing an answer to an open
question whether there exists a von Neumann regular ring which is not
separative.
  The paper concludes with an example of an open question whether every totally
nonnegative matrix is a product of nonnegative idempotent matrices.
