References: An Elementary Proof that Reduced Row Echelon form of a Matrix is Unique

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Lay, D., Lay, S., McDonald, J. (2016). Linear Algebra and its Applications, 5th ed. Boston: Pearson.
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MacCluer, C. (2006). An Elementary Proof of the Uniqueness of the Row-Reduced Echelon Form. Available at https://www.researchgate.net/publication/323539315. Online preprint.
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Meyer, C. D. (2010). Matrix Analysis and Applied Linear Algebra. Philadelphia, PA: SIAM.
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Thomas, Y. (1984). The reduced row echelon form of a matrix is unique: A simple proof. Math. Mag. 57(2): 93–94.
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