Corollary 2
Tag 05NU, permanent. Cite it as [Bourbaki, Tag 05NU].
Algebra, chapter II, § 2. Modules of linear mappings. Duality
If E is a free A-module with a finite basis, every finite basis of E is the dual basis of a basis of E.*
It suffices to consider in E the dual basis of the given basis and canonically to identify E with E.
Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.
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