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What would be the probability of matrix having determinant zero out of all matrices with all entries being positive? How does one calculate such?

Edit: Restriction to natural numbers and size of $n \times n$. Restriction to entries from 0 to 5 or from 0 to 10.

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    For an example of a version of this question that has a simple answer, see http://math.stackexchange.com/questions/54246.2012-12-10

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If the possible elements belong to an infinite set such as natural numbers, real numbers or complex numbers, then the probability is 0 simply because the space of matrices with determinant 0 is a subspace of all matrices.

If they belong to a finite set, then the probability is between 0 and 1 but most likely so small and gets even smaller as your set grows.