Assume X is an invertible $n \times n$ matrix with all entrances different from zero.
I was wondering: can its inverse have a zero in some entrance?
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1Yes, say $A = \begin{bmatrix} 3 & 7 & 0 \ 6 & 4 & 7 \ 5 & 8 &10 \end{bmatrix}$, so $\det(A) = -223 \ne 0$, but $A^{-1}$ has no zero entries. – GNUSupporter 8964民主女神 地下教會 Apr 24 '18 at 14:43
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I was thinking of the other case around. A has no zero entrances but $A^{-1}$ has. – jpugliese Apr 24 '18 at 14:55
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1@jpugliese: the inverse of the inverse of $A$ is $A$. – Martin Argerami Apr 24 '18 at 14:59
