## 每週問題 May 15, 2017

Let $A$ be an $n\times n$ skew-symmetric matrix. Prove that $\hbox{adj}A$ is a symmetric matrix for odd $n$ and a skew-symmetric matrix for even $n$.

$(\hbox{adj}A)^T=\hbox{adj}(A^T)=\hbox{adj}(-A)=(-1)^{n-1}\hbox{adj}A$

$n$ 為奇數，則 $(\hbox{adj}A)^T=\hbox{adj}A$；若 $n$ 為偶數，則 $(\hbox{adj}A)^T=-\hbox{adj}A$