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If A^(-1)=[{:(1,-2),(-2,2):}], what is d...

If `A^(-1)=[{:(1,-2),(-2,2):}]`, what is det (A) ?

A

2

B

-2

C

`(1)/(2)`

D

`-(1)/(2)`

Text Solution

Verified by Experts

The correct Answer is:
D
We know that det (A) = `(1)/(det(A^(-1)))`
`A^(-1)=[{:(1,-2),(-2," "2):}]`
`rArr |A^(-1)|=|{:(1,-2),(-2," "2):}|2-4 =-2 rArr det(A)=-(1)/(2)`
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