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Jim Humphreys
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Maybe I can comment on Question 2. To me the essential point is that this kind of result belongs to elementary linear algebra and basic group theory rather than to geometric algebra. Generation of special linear groups (or slightly larger groups) by involutions probably goes back a long way and may have multiple origins, though I don't have a definitive reference handy. (I'd probably try to ask someone like Gustafson or Djokovic rather than search the scattered literature.)

From a semi-modern viewpoint, for instance, generation of a general linear group over an arbitrary field focuses on the traditional building blocks: elementary, permutation, and diagonal matrices. Since a one-parameter group of elementary matrices along with a suitable permutation matrix will generate a copy of SL$_2$, generation of a special linear group just requires these two kinds of ingredients. Here a permutation matrix is obviously a product of involutions. On the other hand, SL$_2$ is almost simple, while its subgroup generated by involutions is obviously normal and too big to be the center. (To include matrices of determinant $-1$ is a further step.)

Books like those by Dieudonne (and Artin) mix in further ideas arising from the geometry of a bilinear form, along with consideration of exact upper bounds on the number of involutions needed to generate any group element. Such upper bounds for products of involutions in general linear groups may have come along later, but already in 1967 Djokovic observed in an Arch. Math. note that an invertible matrix is the product of two involutions iff it is similar to its inverse.

Jim Humphreys
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