Question

设A,B为n阶方阵,A*为A的伴随矩阵.若|A|=-2,|B|=-3,则|A*B^-1|=_______

Answer 1

|A^-1B*-A*B^-1|

= |A^-1(B*B-AA*)B^-1|

= |A^-1| |(|B|E-|A|E)| |B^-1|

= -(1/6) |(|B|-|A|)E|

= -(1/6) |-5E|

= -(1/6)* (-5)^n