Matrix/Elementary row operation/Definition

Let ${\displaystyle {}K}$ be a field, and let ${\displaystyle {}M}$ be an ${\displaystyle {}m\times n}$-matrix over ${\displaystyle {}K}$. The following manipulations on ${\displaystyle {}M}$ are called elementary row operations.

1. Transpositions of two rows.
2. Multiplication of a row with a scalar ${\displaystyle {}s\neq 0}$.
3. Addition of ${\displaystyle {}a}$ times a row to another row.