Question

已知三阶矩阵A的逆矩阵为A^-1=1 0 0 求伴随矩阵的逆矩阵 求详细过程···· 1 1 -1 1 3 -2,

Answer 1

A^-1 =
1 0 0
1 1 -1
1 3 -2

解: 由 AA* = |A|E 得 A* = |A|A^-1
所以有 (A*)^-1 = (1/|A|) A
而 |A| = 1*(-2+3) = 1
所以 (A*)^-1 =
1 0 0
1 -2 1
2 -3 1

追问

A是怎么得出来的啊

追答

A = (A^-1)^-1

(A^-1,E) =
1 0 0 1 0 0
1 1 -1 0 1 0
1 3 -2 0 0 1

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

r3-3r2
1 0 0 1 0 0
0 1 -1 -1 1 0
0 0 1 2 -3 1

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

所以 A=
1 0 0
1 -2 1
2 -3 1