设A,B为同阶方阵，则（AB）*=？ 急！

Question

如题所述

Answer 1

知识点: 对任一n阶方阵A, 总有 AA*=A*A=|A|E

当A,B可逆时
|A||B|B*A*
= |AB|E(B*A*)
= (AB)*AB(B*A*)
= (AB)*A(BB*)A*
= (AB)*A|B|EA*
= |A||B|(AB)*.
∵ |A|≠0,|B|≠0,
∴ (AB)*=B*A*.