Corollary

Tag 064C, permanent. Cite it as [Bourbaki, Tag 064C].

Algebra, chapter III, § 8. Determinants

Two similar square matrices have equal determinants.

If P is an invertible square matrix, then $\det(PXP^{-1}) = \det X$ by (8) and (9).

Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.

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