If det != 0 ⇐> matrix inverse exists.
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Determinants measure factor of area change.
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Matrix inverses are basically like playing the matrix operation in reverse.
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If the determinant of a certain matrix is zero, then that operation squishes the grid into a lower dimension (so into a line, into a plane, into a point etc).
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If the entire universe is squished into a single point, then the reverse will have to be a one-to-many operation as we would be re-expanding the entire universe.
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This makes that reverse operation non-functional ⇒ not a matrix ⇒ the inverse does not exist.