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revBot (Created page with "<div class="d-none"><math> \newcommand{\mathds}{\mathbb}</math></div>Prove with full details, based on the above, that the determinant of the systems of vectors <math display="block"> \det:\mathbb R^N\times\ldots\times\mathbb R^N\to\mathbb R </math> is multilinear, alternate and unital, and unique with these properties. Then try to prove as well this directly, without any reference to geometry.")Apr 20'25 at 1:29+398