Product decomposition of a nonnegative matrix

Question

Suppose $A\neq 0$ is a nonnegative matrix which can be decomposed as $BC$ with $B\neq 0$ nonnegative and $C$ orthogonal. Then, is $C$ also nonnegative?

I think yes. The case when $B$ is invertible is trivial. But, if $B$ is not invertible, it does not seem obvious. Any hints? Thanks beforehand.

Answer 1

No. For example, if $A = B = 0$, then $C$ can be anything.