If $ A $ and $ B $ are square matrices of order $ 3 $ such that $ |A|=3 $ and $ |B|=2 $, then the value of $ \left|A^{-1} a d j B^{-1} a d j\left(3 A^{-1}\right)\right| $ is equal to

Question

If $ A $ and $ B $ are square matrices of order $ 3 $ such that $ |A|=3 $ and $ |B|=2 $, then the value of $ \left|A^{-1} a d j B^{-1} a d j\left(3 A^{-1}\right)\right| $ is equal to, $ 27 $, $ \frac{27}{4} $, $ \frac{1}{108} $, $ \frac{1}{4} $

MARKS App · Accepted Answer

A - 1 a d j B - 1 a d j 3 A - 1 = A - 1 a d j B - 1 a d j 3 A - 1 = 1 A B - 1 2 × 3 A - 1 2 = 1 A × 1 B 2 × 3 6 A 2 = 3 6 3 3 × 2 2 = 27 4

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