由已知 A*BA=2BA-8E
等式两边左乘A,右乘 A^-1
得 |A|B = 2AB - 8E
又因为 |A| = 1*(-2)*1 = -2
所以 -2B = 2AB - 8E
所以 (2A+2E)B = 8E
所以 B = 4(A+E)^-1 = 4 diag(2,-1,2)^-1 = 4 diag(1/2,-1,1/2) = diag( 2,-4,2)