$\text{rank}(A) = \dim(\text{Row}(A))$ and $\text{rank}(A) = \dim(\text{Col}(A))$

$\text{rank}(A) = \dim(\text{Row}(A))$ but $\text{rank}(A) \neq \dim(\text{Col}(A))$

$\text{rank}(A) + \dim(\text{Row}(A)) = m$

$\text{rank}(A) = m + n - 1$