Question

设A为三阶方阵，行列式|A|=2，A*是A的伴随矩阵，则|(A/4)^-1+A*|=? 求过程,在线等```

Answer 1

解: A* = |A|A^-1 = 2A^-1
(A/4)^-1 = 4A^-1
所以
|(A/4)^-1+A*|
= |4A^-1+2A^-1|
= |6A^-1|
= 6^3 |A^-1|
= 6^3/2
= 108