Assuming that it holds when n=k, then when n=k+ 1, let |A| have two rows of the same order k+ 1.

decisive factor

, as long as it is proved that |A|=0.

In fact, it is to let the I line of A, like the J line, expand into |A| in the first column. By induction, suppose a_{l 1}(l is not equal to I, j).

Algebraic cofactor

0, then | a | a | = 0 A _ {I 1} a _ {I1}+a _ {j1} a _ {j1}, because the I line of A is the same as the J line, then a _ {