What is the meaning of the matrix determinant?

Question

When studying linear algebra, you are constantly dealing with determinants. I read their definition on Wikipedia, saw all kinds of formulas, but found that if someone will ask me WHAT EXACTLY is a matrix determinant, I could not answer. All people who know math answered this question to me like this: "Well, this is such a thing, here is the formula to calculate it, it is very important in linear algebra." I understand that a determinant is the volume (or area) of a figure formed by vectors. I can’t understand why someone came up with the idea to use them. I realize that the question sounds like a request to explain the multiplication, and yet I ask it, since I am very curious about what a determinant really is. If possible, answer as detailed and exhaustive as possible.

You should remove "If possible, answer as detailed and exhaustive as possible.". — , Apr 16 '20 at 14:45
There is a video of 3blue1brown on it, do check it on youtube — , Apr 16 '20 at 14:45
Does this answer your question? What is the origin of the determinant in linear algebra? — , Apr 16 '20 at 14:49
Counterintuitive answer:
http://www.axler.net/DwD.html

Perhaps if you could see all the ideas developed without determinants, it would allow you to step back and appreciate how the determinant connects the ideas. — , Apr 16 '20 at 14:53
Once answer to the question of "what is a determinant" is "it is an $n$-linear function on an $n$-dimensional vectors space, normalized so that $\det(I) = 1$". — Ben Grossmann, Apr 16 '20 at 14:55

What is the meaning of the matrix determinant?

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