Matrix/Row rank and column rank/Manipulations/Fact

Let ${\displaystyle {}K}$ be a field, and let ${\displaystyle {}M}$ denote an ${\displaystyle {}m\times n}$-matrix over ${\displaystyle {}K}$.

If ${\displaystyle {}M}$ is transformed with elementary row manipulations to a matrix ${\displaystyle {}M'}$ in the sense of fact, then the rank equals the number of relevant rows of ${\displaystyle {}M'}$.