Question

设A为n阶可逆矩阵，证明（A*）-1=|A|^-1*A

设A为n阶可逆矩阵，证明（A*)^-1=|A|^-1*A

Answer 1

A A* = |A|E
(A/|A|) A* = E
所以A*的逆矩阵是A/|A|

Answer 2

因为
A^(-1)=A*/|A|
(A*)^(-1)=A/|A|