Question

A为三阶方阵,已知|A|=3,求|A*-8A^-1|

Answer 1

A* = |A|A^-1 = 3A^-1

所以 |A*-8A^-1|

= |3A^-1 - 8A^-1|

= |-5A^-1|

= (-5)^3 |A^-1|

= -125 / |A|

= -125/3.