很简单,用如下定理:
A*Adj(A)=det(A)E .(1)
(1)两边右乘(Adj(A)的逆)得
A = det(A) (Adj(A)的逆) ...(2)
(1)两边同取行列式得
det(A) * det(Adj(A)) = det(A)^3
故 det(Adj(A)) = det(A)^2 .(3)
先求det(A).由题设知det(Adj(A)) = 21+12-12-12=9,所以由(3)知det(A) = 3或-3.
又 (Adj(A)的逆) = Adj(Adj(A)) / det(Adj(A))
= -3 9 6 / 9
0 -6 3
3 0 -6
所以由(2)知 A = -1 3 2 或 1 -3 -2
0 -2 1 0 2 -1
1 0 -2 -1 0 2