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Question

In a square matrix ‘A’ of order 3, ‘aii’s are the sum of the roots and ‘ai, i+1’s are the product of the roots of the equation x2 – 5x + 6 = 0; ai, i1’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___

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Solution

Given a11=a22=a33=a+b, a12=a23=abdet(A)=∣ ∣a+bab01a+bab01a+b∣ ∣=(a2+b2)(a+b)(a+b=5, ab=6)

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