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This question cropped up as a part of my research. Let us assume a $n\times n$ random matrix $\mathbf{M}$ with elements iid distributed to a Bernoulli distribution that takes values $\{0,1\}$ with probability $ \ p = 1/2$.

What I want to know is that what sort of distribution would $\mathbf{M}^{-1}$ have? and what could its possible expectation be?

I have posted this question on math.stackexchange too.

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  • $\begingroup$ There is no reason for the inverse to have entries in $\{0,1\}$. $\endgroup$
    – Alf
    Commented Feb 21, 2021 at 15:18
  • $\begingroup$ Ah yes, I realized that. $\endgroup$
    – Nishant Singh
    Commented Feb 22, 2021 at 3:29
  • $\begingroup$ It seems from row reduction method that the entries of inverse matrix are in $\{±\frac{p}{q}, 0, ±k\}$, for a $n×n$ matrix. Here, $0<p<n-1, 0<q≤n-1 , 0<k≤n-1 $. $\endgroup$
    – Alapan Das
    Commented Feb 22, 2021 at 3:35
  • $\begingroup$ Please don't post in both places so close together. :-) $\endgroup$
    – David Roberts ♦
    Commented Feb 22, 2021 at 4:05
  • $\begingroup$ oh should I delete the one on stackexchange? $\endgroup$
    – Nishant Singh
    Commented Feb 22, 2021 at 5:20

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