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If A=[(alpha, 2),(2, alpha)] and |A^(3)|...

If `A=[(alpha, 2),(2, alpha)]` and `|A^(3)|=27` then `alpha` is equal to

A

`+-sqrt(7)`

B

`+-1`

C

`+-sqrt(5)`

D

`+-2`

Text Solution

Verified by Experts

The correct Answer is:
A
We have `A=[(alpha, 2),(2, alpha)]`
`implies|A|=|(alpha,2),(2,alpha)|=alpha(2)-4`
Now
`implies|A|^(3)=27 [ :'|A^(n)|=|A|^(n)]`
`implies(alpha^(2)-4)^(3)=27[ :' |A|=alpha^(2)-4]`
`impliesalpha^(2)-4=3`
`implies alpha^(2)=7`
`:.alpha=+-sqrt(7)`
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