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:
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.