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Question

Let A=[aij] and B=[bij] be two 3×3 real matrices such that bij=(3)(i+j2)aji, where i,j=1,2,3. If the determinant of B is 81, then the determinant of A is :


A
19
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B
181
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C
13
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D
3
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Solution

The correct option is A 19
bij=(3)(i+j2)aji

B=30a113a2132a313a1232a2233a3232a1333a2334a33

|B|=∣ ∣ ∣30a113a2132a313a1232a2233a3232a1333a2334a33∣ ∣ ∣

Taking 32 common each from C3 and R3
|B|=81∣ ∣ ∣a113a21a313a1232a223a32a133a23a33∣ ∣ ∣

Taking 3 common each from C2 and R2
|B|=81×9∣ ∣a11a21a31a12a22a32a13a23a33∣ ∣

Given |B|=81
81=81×9|A||A|=19

Mathematics

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