determinant of the Vandermonde matrix

Let $R$ be a commutative ring with identity, and fix elements $a_{1},a_{2},...,a_{n}\\in R$ . The determinant of the Vandermonde matrix $\\big{(}(a_{i})^{j-1}\\big{)}_{i,j=1}^{n}$ is equal to the product

\\prod_{1\\leq i<j\\leq n}(a_{j}-a_{i}).

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