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

Sources

• 1982: A.O. Morris: Linear Algebra: An Introduction (2nd ed.) ... (previous) ... (next): Chapter $1$: Linear Equations and Matrices: $1.3$ Applications to Linear Equations: Theorem $1.7$