Remark 2
Tag 00KG, permanent. Cite it as [Bourbaki, Tag 00KG].
Algebra, VIII, p. 338, § 17. Reduced Norms and Traces
From formulas (1), (2), (4), and (6), we deduce the relation and therefore another proof of the Cayley–Hamilton theorem (III, §8, No. 11, p. 541).
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.