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Implication

Let A=[ p q...

Question

Let $A = [\begin{matrix} p & q q & p \end{matrix}]$ such that $d e t (A) = r$ where $p, q, r$ all prime numbers, then trace of $A$ is equal to

6

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5

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2

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Solution

The correct option is A $6$
Let $(A) = p^{2} - q^{2} = r$
$(p + q) (p - q) = r$
r = prime
$∴ p - q = 1$
So,
$P = 3, q = 2$ ( $∵ p, q \equiv$ prime)
and $t r a c e$ (A) = 2p = 6$

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