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Q.

Let A, B, C, D be non singular matrices of order 3×3  such that (AAT)BC2=BT and C2=I  and D is an orthogonal matrix such that  AT and D commute with each other and  DTATD=A1, then

Column-I

Column-II

A)

If  B=B1, then |B2018C|  can be equal to

P)

–1

B)

If (ACAT)2019=ACKAT  then k can be equal to

Q)

0

C)

|ACAT| can be equal to

R)

2

D)

|BBT(B1)2|+|(AAT)2018|  is equal to

S)

3

 

 

T)

4

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a

A  P, B  S, C  R, D  R

b

A  P, B  R, C  S, D  P

c

A  S, B  P, C  R, D  P

d

A  P, B  S, C  P, D  R

answer is B.

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Detailed Solution

detailed_solution_thumbnail

 ATD=DAT
DDT=DTD=I 
DDTATD=DATDA1=DATA1=AT 
BC2=BTB=BT 
(A)       B=B1B2=I
 |B2018C|=|C|=±1
(B) (ACAT)2019=(ACAT)(ACAT).......(ACTT)=AC2019AT=ACkATk
is odd
(C)  |ACTT|=|A|2|C|=|C|=±1
(D)  |BBT(B1)2|+|(AAT)2018|=1+1=2

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