Question

设a b为n阶方阵 且|A|≠0 |E-AB|≠0证明|E-BA|≠0在线等,

Answer 1

简单计算一下即可，详情如图所示

Answer 2

因为 |A|≠0,所以A可逆
因为 E-BA = A^-1(E-AB)A
所以 |E-BA| = |A^-1| |E-AB| |A| = |E-AB| ≠0