# pr.probability – Distribution and Expectation of Inverse of a Random Bernoulli Matrix

This question cropped up as a part of my research. Let us assume a $$ntimes n$$ 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?

My guess so far has been that the distribution remains the same. I have posted this question on math.stackexchange too.