Suppose it holds when n=k, and when n=k+ 1, let |A| be a determinant of order k+ 1 with two identical rows, as long as it is proved that |A|=0.

In fact, it is to let the I line of A expand |A| according to the first column, just like the J line. By induction, if the algebraic remainder of a_{l 1}(l is not equal to I, j) is 0, then | a |A|=0 A _ {I 1} A _ {I65438+.