题目有误,不是行列式的逆矩阵,而是矩阵的逆矩阵.
（A,E）=
[1 1-1 100]
[0 2 2 010]
[1-1 0 001]
行初等变换为
[1 1-1 100]
[0 2 2 010]
[0-2 1-101]
行初等变换为
[1 1-1 100]
[0 2 2 010]
[0 0 3-111]
行初等变换为
[1 1 0 2/31/31/3]
[0 2 0 2/31/3 -2/3]
[0 0 1-1/31/31/3]
行初等变换为
[1 0 0 1/31/62/3]
[0 1 0 1/31/6 -1/3]
[0 0 1-1/31/31/3]
得逆矩阵 A^(-1)=
[ 1/31/62/3]
[ 1/31/6 -1/3]
[-1/31/31/3]