Definition:Inverse of Elementary Column Operation
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Definition
Let $e$ be an elementary column operation which transforms a matrix $\mathbf A$ to another matrix $\mathbf B$.
Let $e'$ be an elementary column operation which transforms $\mathbf B$ back to $\mathbf A$.
Then $e'$ is the inverse of the elementary column operation $e$.
Also see
- Existence of Inverse Elementary Column Operation which demonstrates that $e'$ always exists for a given $e$.