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Question

A = qrp(q+r)pr+pqpq+qrprpq+qrqr+prqr+prpq then |A| equals:

A
(pq)2
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B
(p2q2)2
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C
[(qr)3]
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D
(pq)3
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Solution

The correct option is D (pq)3
A = qrp(q+r)pr+pqpq+qrprpq+qrqr+prqr+prpq
|A| = ∣ ∣ ∣qrp(q+r)pr+pqpq+qrprpq+qrqr+prqr+prpq∣ ∣ ∣
applying R1R1+R2+R3 gives
(pq+qr+pr)∣ ∣111pq+qrprpq+qrqr+prqr+prpq∣ ∣
applying C1C1C3 and expanding gives
(pq+qr+pr)∣ ∣0110prpq+qrpq+qr+prqr+prpq∣ ∣=(pq+qr+pr)3
|A|=(pq+qr+pr)3
Hence, option D.

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