If we have matrix $A\in Mat_{n}(\mathbb{R})$ with property $A^{2}=-I$. How to show n must be even?
Question about negative matrix involution
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4The shortest way is to take the determinant of both sides. – 2011-10-26
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Just take the determinant on both sides. You get $\det (A)^2 = (-1)^n$.