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If A=[alphabetagamma-alpha] is such that...

If `A=[alphabetagamma-alpha]` is such that `A^2=I` , then `1+alpha^2+betagamma=0` (b) `1-alpha^2+betagamma=0` (c) `1-alpha^2-betagamma=0` (d) `1+alpha^2-betagamma=0`

A

`1+alpha^(2)+betagamma =0`

B

`1-alpha^(2) +beta gamma =0`

C

`1-alpha^(2)-beta gamma=0`

D

`1+alpha^(2)-beta gamma =0`

Text Solution

Verified by Experts

The correct Answer is:
A
`A^(2) =I`
`implies [{:(alpha,beta),(gamma,-alpha):}][{:(alpha,beta),(gamma,-alpha):}]=I`
`implies[{:(alpha^(2)+betagamma,alphabeta-betaalpha),(gammaalpha -alphagamma,betagamma +alpha^(2)):}]=I`
`implies [{:(alpha^(2) +beta gamma ,0),(0, alpha^(2) +betagamma ):}]=[{:(1,0),(0,1):}]`
`alpha^(2) +beta gamma =1 implies 1-alpha^(2) -betagamma =0`
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