Question

已知A和B是同阶可逆矩阵,证明(AB)*=B*A*

Answer 1

AA* = |A|E ; A* = |A|A-1
(AB)* =|AB|(AB)-1 = |A||B|(B-1)(A-1) = {|B|B-1}{|A|A-1} = B*A*