The following is an exercise.
Suppose that $A$ is an $n\times n$ matrix and that $m$ rows of $A$ are selected to form an $m\times n$ submatrix $B$. By considering the number of zero rows in the normal form, prove that $\text{rank}B \ge m - n + \text{rank} A$.
My solution showed that $A$ could also be a non-square matrix and the result would still follow. Is my observation correct?