---
about:
- 0WF5AQYTW6
kind: statement
msc:
- 15A06
name: Uniqueness of the reduced row echelon form
role: theorem
sources:
- locator: src/section1-2.xml:1343
  url: https://github.com/davidaustinm/ula/blob/b6ea263ef23703072b7007485bb7a2d89c5f399b/src/section1-2.xml#L1343
tag: BF9SMZMJZE
uses:
- 0WF5AQYTW6
- 095DDGZF16
---

## Statement

Let $A$ be a matrix. Then there is exactly one matrix in [[reduced row echelon form|0WF5AQYTW6]] that is [[row equivalent|095DDGZF16]] to $A$.

## Remarks

Existence comes from row reduction. The content of the result is that two different reduced row echelon matrices are never row equivalent to the same matrix. So the reduced row echelon form of $A$ is well defined, and two matrices are row equivalent exactly when they have the same one.