证明下列行列式.

D=D1+D2
D1=
| a² a 1/a 1 |
| b² b 1/b 1 |
| c² c 1/c 1 |
| d² d 1/d 1 |
=
| a 1 1/a² 1/a |
(abcd)*| b 1 1/b² 1/b |
| c 1 1/c² 1/c |
| d 1 1/a² 1/d |
=
| a 1 1/a² 1/a |
| b 1 1/b² 1/b |
| c 1 1/c² 1/c |
| d 1 1/d² 1/d |
D2=
| 1/a² a 1/a 1 |
| 1/b² b 1/b 1 |
| 1/c² c 1/c 1 |
| 1/d² d 1/d 1 |
=
| a 1 1/a² 1/a |
(-1)³| a 1 1/b² 1/b |
| a 1 1/c² 1/c |
| a 1 1/d² 1/d |
∴D=D1+D2=0D2前面为什么是（-1∧3）作了三次列交换