Determinant/Zero, linear dependent and rank property/Fact

Let $K$ be a field, and let $M$ denote an $n\times n$-matrix over $K$. Then the following statements are equivalent.

1. We have $detM\ne 0$.
2. The rows of $M$ are linearly independent.
3. $M$ is invertible.
4. We have $\mathrm{rk}M=n$.

Proof, Write another proof