Question

In a square matrix ‘A’ of order 3, ‘$a_{ii}$’s are the sum of the roots and ‘$a_{i,i+1}$’s are the product of the roots of the equation $x^2$ – 5x + 6 = 0; $a_{i,i-1}$’s are all unity and the rest of the elements are all zeros. The value of the determinant (A) is equal to ‘k’. The least prime number that divides it is___

Answer 1

$Given{a}_{11}=a_{22}=a_{33}=a+b,a_{12}=a_{23}=abdet\left(A\right)=\left|\begin{array}{ccc}a+b& ab& 0\\ 1& a+b& ab\\ 0& 1& a+b\end{array}\right|=(a^2+b^2)(a+b)(a+b=5,ab=6)$