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.