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Let A be an nxn matrix with random independent 0 or1 entries. What is the probability that A has zero determinant, as a function of n?

Without thinking, I would have guessed that the probability quickly decreases with n. But for n = 1 the probability is 50%, and for n = 2, surprise, it is 10/16 = 61.5%.

So I revised my guess to be "the probability of the determinant being zero tends to 1 as n goes to oo". 🧵>