If \( \mathrm{A} \) is an invertible matrix of order 3 and \( \mathrm{B} \) is another matrix of...

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If \( \mathrm{A} \) is an invertible matrix of order 3 and \( \mathrm{B} \) is another matrix of the same order as of \( \mathrm{A} \), such that \( |\mathrm{B}|=2, \mathrm{~A}^{\mathrm{T}}|\mathrm{A}| \mathrm{B}=\mathrm{A}|\mathrm{B}| \mathrm{B}^{\mathrm{T}} \). If \( \mid \mathrm{AB}^{-1} \) adj \( \left(\mathrm{A}^{\mathrm{T}} \mathrm{B}\right)^{-1} \mid=K \) then the value of \( 4 \mathrm{~K} \) is equal to
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