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I'm struggling to find a visually intuitive proof for the formula of a 3x3 matrix.

I searched it online for hours and it seems impossible to find a source that attempt at least to explain where does it come from.
I'm aware that a very similiar question has been asked but it's a very old question and it probably didn't get the deserved attention (I'm referring to this). Moreover, I think that the increased popularity of the site since then may offer this question the possibility to get a better and more satisfactory answer which would turn helpful for a lot of students.

This what a visual explanation for the determinant's formual of a 2x2 matrix: enter image description here

This makes it very clear why determinant for a 2x2 matrix is ad-bc and it visually explains how determinant is linked to the area of a parallelogram.
I'm not looking necessarly for this kind of "geometric" proof.
It would be helpful any intuitive explanation for the formula.

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    $\begingroup$ This might be what you're looking for. math.stackexchange.com/questions/427528/… $\endgroup$ – tch Jan 9 at 18:55
  • $\begingroup$ Isn't the attached figure a strong evidence that explaining determinant this way is rather unintuitive? To be frank, I don't understand why people are so obsessed with geometric interpretations when linear algebra is concerned. Certainly there are useful geometric interpretations at times, but not everything is geometric in nature or best understood from a geometric perspective. $\endgroup$ – user1551 Jan 9 at 23:12

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