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If A is a square matrix of order 3 such ...

If A is a square matrix of order 3 such that `det(A)=(1)/(sqrt(3))` then `det(Adj(-2A^(-2)))` is equal to

A

24

B

16

C

576

D

144

Text Solution

Verified by Experts

The correct Answer is:
C
`therefore|Adj(-2A^(-2))|=|-2A^(-2)|^(2)` ...(1)
`because|-2A^(2)|=(-2)^(3)|A^(-2)|=(-8)|A^(-1))^(2))(-8)|A^(-1)|^(2)`
`=(-8)((1)/(|A|))^(2)=(-8)xx(1)/((1)/(3))=-24`
`therefore` from equation (1)
`|Adj(-2A^(-2))|=(-24)^(2)=576`
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