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Feb 2, 2022 at 17:18 comment added T. Amdeberhan Thank you, indeed.
Feb 2, 2022 at 16:58 comment added Ofir Gorodetsky Your matrix is anti-symmetric. The determinant of any odd anti-symmetric matrix is 0, and the determinant of any even anti-symmetric matrix is a square (known as the Pfaffian). The first part is completely elementary and follows from applying the determinant to the identity $A=-A^T$, while the second part is due to Cayley and has several proofs.
Feb 2, 2022 at 16:53 history edited T. Amdeberhan CC BY-SA 4.0
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Feb 2, 2022 at 16:28 history asked T. Amdeberhan CC BY-SA 4.0