因为A,B是正交矩阵
所以 AA^T=A^TA=E,BB^T=B^TB=E
又因为 |A||B|=-1
所以 - |A+B|
= - |(A+B)^T|
= - |A^T+B^T|
= |A||A^T+B^T||B|
= |AA^TB+AB^TB|
= |B+A|
= |A+B|
所以 |A+B| = 0.