求矩阵A=1 -1 0 0 1 1 2 -1 2的逆矩阵

题目

求矩阵A=1 -1 0 0 1 1 2 -1 2的逆矩阵

答案

(A,E)=
1 -1 0 1 0 0
0 1 1 0 1 0
2 -1 2 0 0 1

r3-2r1
1 -1 0 1 0 0
0 1 1 0 1 0
0 1 2 -2 0 1

r3-r2
1 -1 0 1 0 0
0 1 1 0 1 0
0 0 1 -2 -1 1

r2-r3,r1+r2
1 0 0 3 2 -1
0 1 0 2 2 -1
0 0 1 -2 -1 1

A^-1 =
3 2 -1
2 2 -1
-2 -1 1

是否正确, 与A相乘看是否等于E即知.