Remark 2

Tag 00LS, permanent. Cite it as [Bourbaki, Tag 00LS].

Algebra, VIII, p. 362, § 19. Quaternion Algebras

The quaternion algebra of type $(\alpha ,0, \gamma )$ is isomorphic to the quaternion algebra of type $(\gamma ,0, \alpha )$ (III, §2, No. 5, p. 445). It is also isomorphic to the quaternion algebra of type $(\alpha a^2,0, \gamma c^2)$ for every pair $(a, c)$ of nonzero elements of K.

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.

Cited by

Theorem 1, § 19

Cites

III, §2, No. 5, p. 445