Singular matrices are a cornerstone of Linear Algebra with significant theoretical and practical implications. Motivated by a classroom discussion, I investigated the probability of a randomly generated 2×2 matrix being singular when its entries are restricted to natural numbers less than or equal to a given value 𝑛. By approaching the problem geometrically, I derived a combinatorial formula to determine this probability. To validate the formula, I wrote a program that confirmed my formula for the first 20 natural numbers. Restricting the possible entries of the matrix to natural numbers produced a finite number of matrices from which the proportion of the number of singular matrices could be determined.