Examples of matrices that are both skew-symmetric and orthogonal – math.stackexchange.com

Examples of matrices that are both skew-symmetric and orthogonal – math.stackexchange.com

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Are there matrices that satisfy these two conditions? That is, a matrix $A$ such that $$A^T=A^{-1}=-A$$ What I know is that a skew symmetric matrix with $n$ dimensions is singular when $n$ is odd.

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