Geodesic
From a linear system through geometry to a determinant
Matematičeskoe obrazovanie, no. 3 (2021), pp. 70-85 
I. B. Pisarenko; M. I. Zaidel. From a linear system through geometry to a determinant. Matematičeskoe obrazovanie, no. 3 (2021), pp. 70-85. http://geodesic.mathdoc.fr/item/MO_2021_3_a7/
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     author = {I. B. Pisarenko and M. I. Zaidel},
     title = {From a linear system through geometry to a determinant},
     journal = {Matemati\v{c}eskoe obrazovanie},
     pages = {70--85},
     year = {2021},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MO_2021_3_a7/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

The article proposes some reasoning that allows us to introduce a definition of the determinant of a matrix (as well as some other concepts) in a natural way. In this case, the properties of the determinant become self-evident.

[1] G. Strang, Introduction to Linear Algebra, 5th Edition, Cambridge Press, Wellesley, USA, 2016, 574 pp. | Zbl

[2] G. Strang, Gilbert Strang lectures on Linear Algebra (MIT), pleilist videozapisei lektsii G. Strenga, , 2005 https://www.youtube.com/playlist?list=PL49CF3715CB9EF31D | Zbl