1 0 0
1 1 - 1
- 1 0 1
Solution: AA' =
1 0 0
3 1 -2
-2 0 - 1
(AA ',E)= 1
1 0 0 1 0 0
3 1 -2 0 1 0
-2 0 - 1 0 0 1
r2-3r 1,r2+2r 1
1 0 0 1 0 0
0 1 -2 -3 1 0
0 0 - 1 2 0 1
R3 *( 1),r2+2r3
1 0 0 1 0 0
0 1 0 -7 1 -2
0 0 1 -2 0 - 1
So (aa')- 1 =
1 0 0
-7 1 -2
-2 0 - 1
If you are satisfied, please adopt it.