即，a, =au，j=1,2,,n,于是，D- Z (-1)auy-.m.ji..jn- E (-..ji..jn= E --1)ax.m.ji...jn- E (-am.jii...jn=-D:. D=0.区区下S2.4行列式的性质§2.4 行列式的性质, 1,2, , , ij kj a a j n = = 1 1 2 1 2 ( ) 1 2 ( 1) i k n i k n n j j j j j j ij kj nj j j j D a a a a a  = −  即， 1 1 2 1 2 ( ) 1 2 ( 1) i k n i k n n j j j j j j kj ij nj j j j a a a a a  = −  1 1 2 1 2 ( ) 1 2 ( 1) k i n k i n n j j j j j j ij kj nj j j j a a a a a  = − −  1 1 2 1 2 ( ) 1 2 ( 1) k i n k i n n j j j j j j ij kj nj j j j a a a a a  = − −  = −D  = D 0. 于是