Show that AB is a zero matrix, provided θ − ϕ is an odd multiple of π over 2

212,760 • May 25 2022
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Question 7. If {\displaystyle A = { \begin{bmatrix} {\cos^2\theta} & {\cos \theta \sin \theta} \\ {\cos \theta \sin \theta } & {\sin^2 \theta} \end{bmatrix} } } , {\displaystyle B = {\begin{bmatrix} {\cos^2 \phi} & { \cos \phi \sin \phi } \\ {\cos \phi \sin \phi } & {\sin^2 \phi } \end{bmatrix}} } then show that AB is a zero matrix, provided {\displaystyle (\theta  - \phi )} is an odd multiple of {\displaystyle \frac{\pi }{2}} .