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If \( A \& B \) are two non singular matrices of order \( 3 \times 3 \) such that \( A^{\mathrm{T}}+\mathrm{B}=\mathrm{I} \& \mathrm{BA} \mathrm{A}^{\mathrm{T}}=-\mathrm{B} \), then which is/are always true (where \( \mathrm{X}^{\mathrm{T}} \) denotes transpose of \( \mathrm{X} \) and \( \mathrm{I} \) denotes unit matrix)-
(A) \( |\mathrm{B}|=2 \)
(B) \( |\mathrm{B}|=8 \)
(C) \( |\mathrm{A}|=-1 \)
(D) \( |\mathrm{A}|=1 \)
(where \( |\mathrm{X}| \) denotes determinant value of \( \mathrm{X} \) )
\( \mathrm{P} \)
W
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