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Q.

If  A=abcxyzpqr,B=q−by−pa−xr−cz and if A is invertible. Then which of the following is true?

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a

|A|=|B|

b

|A|=−|B|

c

|A|=−2|B|

d

|A|=2|B|

answer is B.

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Detailed Solution

|B|=q−by−pa−xr−cz _( multiplying _R2 by-1) =−q    −b    yp    −a    xr    −c    zmultiplying C2 by −1 =qbypaxrcz=−paxqbyrcz=−axpbyqczr=−abcxyzpqr=−|A| Hence |A|=−|B|, obviously when |A|≠0,|B|≠0. Also, ∣ adj B|=|B2=(−|A|)2=|A|2
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