TITLE: Development of the Idea of the Determinant
QUESTION [53 upvotes]: While I basically understand what a determinant is, I wonder how this idea was developed?  What was the principal idea behind its origination?  I would like to know this so that I can have a better conceptualization of the determinant.

REPLY [10 votes]: The authoritative reference seems to be the books by Muir: Contributions to the history of determinants and A treatise on the theory of determinants. See also http://www-history.mcs.st-and.ac.uk/Extras/Muir_determinants.html.
There is also Miller, 
On the History of Determinants. 
Amer. Math. Monthly 37 (1930), no. 5, 216–219.