设A为n阶矩阵,n为奇数,且满足AA^T=E,|A|=1.求|A-E|.
问题描述:
设A为n阶矩阵,n为奇数,且满足AA^T=E,|A|=1.求|A-E|.
如题.
答
|A-E|=|A-AA^T|=|A(E-A^T)|=|A|*|E-A^T| =|(E-A^T)^T|=|E-A|=(-1)^n|A-E|=-|A-E| 所以2|A-E|=0 |A-E|=0