设A为三阶矩阵，且|A|=2，则|2A*-A-1|=272272．

Question

设A为三阶矩阵，且|A|=2，则|2A^*-A^-1|=

(27)/(2)

(27)/(2)

．

Answer 1

由于AA^*=|A|E=2E，因此
|2A^*-A^-1|=(1)/(|A|)|A||2A*−A−1|
=(1)/(2)|A(2A*−A−1)|
=(1)/(2)|2AA*−E|
=(1)/(2)|3E|=(1)/(2)•33＝(27)/(2)