Corollary 1
Tag 005Q, permanent. Cite it as [Bourbaki, Tag 005Q].
Algebra, VIII, p. 82, § 5. Commutation
A free module is balanced.
This is clear if the module is zero, and a nonzero free module is generating (VIII, p. 81, Example 2).
Bourbaki sets the proof directly after the statement, and the corpus does not separate them, so what is above is the statement and its proof together.