Question

If \[ A=\operatorname{Adj}\!\left(-2\left(\operatorname{Adj}(P^{-1})\right)\right) \] and \[ P= \begin{bmatrix} 1& 2& 1 1& 0& 1 0& 1& 2 \end{bmatrix}, \] then \(|A|=\)

• A. \(-\dfrac14\)
• B. \(\dfrac14\)
• C. \(\dfrac34\)
• D. \(\dfrac23\)

Hint:

For an \(n\times n\) matrix, \[ \boxed{ |\operatorname{Adj}(A)|=|A|^{\,n-1} } \] and \[ \boxed{ |kA|=k^n|A|. } \] For a \(3\times3\) matrix, \[ |\operatorname{Adj}(A)|=|A|^2. \]

Answer 1

The Correct Option is B