Suppose we have a square upper triangular matrix $R$, I want to show that it is singular if and only if one of its diagonal elements is zero. I know a matrix is singular if and only if (or is it "if" and not "iff"?) its determinant is zero, right? According to Wikipedia, the determinant of a square matrix ($n \times n$) can be defined by the Leibniz formula or the Laplace formula which I don't understand very well. At the end of that article it says for a lower (upper) triangular matrix the determinant equals the product of the diagonal entries. If it is so, the prove is quite straight forward. But could someone explain to me the reason of the above bold statement?
P.S: I've also read the following questions, but none of them answers my question specifically: