Definition:Inverse of Elementary Row Operation

Definition
Let $e$ be an elementary row operation which transforms a matrix $\mathbf A$ to another matrix $\mathbf B$.

Let $e'$ be an elementary row operation which transforms $\mathbf B$ back to $\mathbf A$.

Then $e'$ is the inverse of the elementary row operation $e$.

Also see

 * Existence of Inverse Elementary Row Operation which demonstrates that $e'$ always exists for a given $e$.


 * Definition:Inverse of Elementary Column Operation