Invertible Matrix Theorem

Given a $n\times n$ matrix $M$, we have the following by the invertible matrix theorem:

$$M\text{ is invertible}⟺\{\begin{array}{l}\text{Col}(M)={\mathbb{R}}^n\\ \dim (\text{Col}(M))=n=\text{rank}(M)\\ \text{Null}(M)=\{\vec{0}\}\\ \dim (\text{Null}(M))=0=\text{nullity}(M)\end{array}$$