Geodesic
From a linear system through geometry to a determinant
Matematičeskoe obrazovanie, Tome 99 (2021) no. 3, pp. 70-85.

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. 
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I. B. Pisarenko; M. I. Zaidel. From a linear system through geometry to a determinant. Matematičeskoe obrazovanie, Tome 99 (2021) no. 3, pp. 70-85. http://geodesic.mathdoc.fr/item/MO_2021_99_3_a7/

[1] G. Strang, Introduction to Linear Algebra, 5th Edition, Cambridge Press, Wellesley, USA, 2016, 574 pp. <ext-link ext-link-type='zbl-item-id' href='https://zbmath.org/?q=an:1351.15002'>1351.15002</ext-link>

[2] G. Strang, Gilbert Strang lectures on Linear Algebra (MIT), pleilist videozapisei lektsii G. Strenga, , 2005 <ext-link ext-link-type='uri' href='https://www.youtube.com/playlist?list=PL49CF3715CB9EF31D'>https://www.youtube.com/playlist?list=PL49CF3715CB9EF31D</ext-link><ext-link ext-link-type='zbl-item-id' href='https://zbmath.org/?q=an:1066.92012'>1066.92012</ext-link>