Matrix/Elementary row operations/Elementary matrix from left/Fact

Let ${}K$ be a field and ${}M$ a ${}n\times n$-matrix with entries in ${}K$.

Then the multiplication by elementary matrices from the left with ${}M$ has the following effects.

1. ${}V_{ij}\circ M=$ exchange of the ${}i$-th and the ${}j$-th row of ${}M$.
2. ${}(S_{k}(s))\circ M=$ multiplication of the ${}k$-th row of ${}M$ by ${}s$.
3. ${}(A_{ij}(a))\circ M=$ addition of ${}a$-times the ${}j$-th row of ${}M$ to the ${}i$-th row (${}i\neq j$).

Write a proof