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If A=[(-cos theta, -sin theta),(-cos the...

If `A=[(-cos theta, -sin theta),(-cos theta, sin theta)]` and `A(adjA)=lamda[(1,0),(0,1)]` then `lamda` is equal to

A

`cos 2 theta`

B

`-sin 2 theta`

C

`- cos 2 theta`

D

`sin 2 theta`

Text Solution

Verified by Experts

The correct Answer is:
B
`:'A(adjA)=|A|l`
`=(-cos theta sin theta-sin theta cos theta)l`
`implieslamda[(1,0),(0,1)]=-2 sin theta cos theta [(1,0),(0,1)]` (Given )
`:.lamda=-sin 2 theta`
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