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If A=[[cosalpha, -sin alpha] , [sin alph...

If `A=[[cosalpha, -sin alpha] , [sin alpha, cos alpha]]` then `A+A'=I` then `alpha=`

A

`(pi)/(6)`

B

`(pi)/(3)`

C

`Pi`

D

`(3pi)/(2)`

Text Solution

Verified by Experts

The correct Answer is:
A
` A=[{:(cos alpha ,-sinalpha),(sin alpha ,cosalpha):}] `
`implies A'=[{:(cosalpha,sinalpha),(-sin alpha,cosalpha):}]`
Now , `A+A'=I`
`implies [{:(cosalpha ,-sinalpha),(sin alpha,cosalpha):}]+[{:(cosalpha,sin alpha ),(-sin alpha ,cos alpha ):}]=[{:(1,0),(0,1):}]`
`implies [{:(2cosalpha,0),(0,2cosalpha):}]=[{:(1,0),(0,1):}]`
`implies 2cos alpha=1`
`implies cos alpha =(1)/(2)`
`alpha=(pi)/(3)`
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