  Generalized Hurwitz theorem states that there are fifteen composition
algebras for any given field: seven unital, six para-unital, and two non-unital
algebras. In this article we explore the recovery of such algebras from 3D
Geometric Algebras. Different involutions, such as reversion, inversion,
Clifford conjugation, and full grade inversion, are introduced in order to
recover the norm of all composition algebras. A special attention is given to
composition algebras of dimension 8, i. e. octonions, para-octonions and Okubo
algebra, for which the introduction of a different product is needed.
