Answer :

Correct answer is : 2

$\left[\begin{array}{cc}3& p\\ p& q\end{array}\right]$,

sum of eigenvalue = 4, product of eigen value = -1

trace of A = 3 + q

sum of eigenvalue = trace of matrix

4 = 3 + q ⇒ q = 1

product of eigen value = determinant of A

-1 = 3q - p²

p² = 3 + 1 = 4

p = ± 2 ⇒ |p| = 2