If and B = bmatrix ^2 & & ^2 bmatrix are two matrices such that is the null matrix

MATHEMATICS · Single correct · CBSE · Mathematics · Matrices · Matrices

Problem

If A=[cos⁡2αcos⁡αsin⁡αcos⁡αsin⁡αsin⁡2α]A = \begin{bmatrix} \cos^2 \alpha & \cos \alpha \sin \alpha \\ \cos \alpha \sin \alpha & \sin^2 \alpha \end{bmatrix} and B=[cos⁡2βcos⁡βsin⁡βcos⁡βsin⁡βsin⁡2β]B = \begin{bmatrix} \cos^2 \beta & \cos \beta \sin \beta \\ \cos \beta \sin \beta & \sin^2 \beta \end{bmatrix} are two matrices such that ABAB is the null matrix, then (1) α=β\alpha = \beta (2) cos⁡(α−β)=0\cos(\alpha - \beta) = 0 (3) sin⁡(α−β)=0\sin(\alpha - \beta) = 0 (4) None of these

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