Algebra – How to prove that rank (A +) is nothing but rank (A)?

look here my friend. How to prove the following equation? Or give a counterexample. thank you so much

$$ text {rank} (A ^ +) leq text {rank} (A) $$

or $ text {rank} (A ^ +) $ represents the positive components of the matrix $ A $, for example.
$$ left[begin{matrix}2 & -1.5 & 0\-2.3 & 2 & 4.1end{matrix}right]^ + = left[begin{matrix}2 & 0 & 0\0 & 2 & 4.1end{matrix}right]. $$