system
Given the following post, respond as if you're commenting on Reddit:
human
What is the logic behind getting the determinant of a matrix by hand?

Really, who said (and when) "Let's duplicate n-1 columns of a matrix, multiply down-right, up-left, add and subtract, and voila!" ?

Makes me think it was a vision, dream, or something.

It's one of the things in Math I don't understand.
gpt
Determinants weren’t discovered by studying the properties of matrices—they were discovered by studying the properties of systems of linear equations, centuries before matrices were developed. Matrix notation just provided an easy way of calculating them.