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Question

If A=[cos2αcosα sinαcosα sinαsin2α] and B=[cos2βcosβ sinβcosβ sinβsin2β] are two matrices such that AB is the null matrix, then


A

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B

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C

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D

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Solution

The correct option is D


AB=0[cos2αcosα sinαcosα sinαsin2α][cos2βcosβ sinβcosβ sinβsin2β]=[0000][cosα cosβ cos(αβ)cosα sinβ cos(αβ)cosβ sinα cos(αβ)sinα sinβ cos(αβ)]=[0000]cos(αβ)=0


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