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Let \( A=\left[\begin{array}{lll}a & b & c \\ b & c & a \\ c & a & b\end{array}\right] \) an \( B=\left[\begin{array}{lll}b c-a^{2} & c a-b^{2} & a b-c^{2} \\ c a-b^{2} & a b-c^{2} & b c-a^{2} \\ a b-c^{2} & b c-a^{2} & a c-b^{2}\end{array}\right] \)
\( \mathrm{P} \)
W. be two non-singular matrices such that \( \left(A^{2}-2 I\right) B=O \) where \( abc0 \), then which of the following statement(s) is(are) CORRECT?
(1) \( T r \cdot(A B)=6 \sqrt{2} \)
(2) \( \operatorname{Tr} \cdot(A B)=-6 \sqrt{2} \)
(3) \( \operatorname{det} \cdot(A-\sqrt{2} B)=54 \sqrt{2} \)
(4) \( \operatorname{det} \cdot(A-\sqrt{2} B)=-54 \sqrt{2} \)
[Note: \( I \) is an identity matrix of order 3 and \( \operatorname{Tr} .(P) \) and det. \( (P) \) denote trace and value of the determinant of square matrix \( P \) respectively.]
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