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Question

If A=122212221
and |(A2pAqI)|=0, then p+q=

A
9
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B
8
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C
7
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D
10
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Solution

The correct option is A 9
A=122212221A2=988898889A2pAqI=9pq82p82p82p9pq82p82p82p9pq|(A2pAqI)|=∣ ∣9pq82p82p82p9pq82p82p82p9pq∣ ∣applying C1C1+C2+C3|(A2pAqI)|=∣ ∣255pq82p82p255pq9pq82p255pq82p9pq∣ ∣applying R2R2R1R3R3R1=∣ ∣255pq82p82p01+pq0001+pq∣ ∣0=(255pq)(1+pq)2qp=1 and 5p+q=25p=4; q=5

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