I am a fan of simple explanations of scientific (or mathematical) concepts. Here is a simple explanation of what is a matrix determinant, about which I have read on Medium.
A 2×2 matrix deforms space, so that a certain area becomes a larger (or smaller) area. The matrix determinant is the ratio of the new area to the old area. A 3×3 matrix deforms volume, so the determinant would be the ratio of the new volume to the old volume.
A negative sign in a determinant of a 2×2 matrix means that the transformation has flipped the area (e.g. swapped the x and y axes).
If a determinant of a 3×3 matrix is 0, it means that the volume is squashed into a flat surface, losing one dimension and making the new “volume” 0. This kind of matrix is not invertible, because information was lost as a result of the transformation and the operation cannot be reversed.
Determinants of higher dimensional matrices are understood by extension.
https://towardsdatascience.com/what-really-is-a-matrix-determinant-89c09884164c
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