Example for $3\times 3$: $A=\begin{bmatrix}0&3&0\\1&0&7\\0&1&0\end{bmatrix}$
I tried out some examples and it seems right, but I honestly have no idea how to prove that it is not invertible in general; any help is really appreciated.
2026-04-25 02:19:37.1777083577
Let $A$ be a square matrix with all its diagonal and anti-diagonal elements equal to zero; is $A$ not invertible?
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How about $\pmatrix{0&1&0&0\\1&0&0&0\\0&0&0&1\\0&0&1&0}$?