Thanks a lot!!!

- Sep 4th 2007, 01:30 PMseekorHow to prove: A,B are orthogonal matrices, if det(A)+det(B)=0, then A+B is singular.
Thanks a lot!!!

- Sep 4th 2007, 02:57 PMtopsquark
- Sep 4th 2007, 06:06 PMJakeD
In general, $\displaystyle det(A + B) \ne det(A) + det(B).$

Example: $\displaystyle A = \begin{pmatrix} 1 & 0 \\ 0 & 0 \end{pmatrix},\ B = \begin{pmatrix} 0 & 0 \\ 0 & 1 \end{pmatrix},\ det(A) = det(B) = 0,\ det(A+B) = 1. $

For square matrices, $\displaystyle det(AB) = det(A)det(B).$ - Sep 5th 2007, 06:43 AMtopsquark