Let where α ∈ R . Suppose Q = [ q ij ] is a matrix such that PQ = kI , where k ∈ R , k ≠…

Mathematics · JEE Advanced · NTA Exams — Matrices and Determinants

Let where α ∈ R. Suppose Q = [q_ij] is a matrix such that PQ = kI, where k ∈ R, k ≠ 0 and I is the identity matrix of order 3. If \(q_{23}=-\frac{k}{8}\) and \(\operatorname{det}(Q)=\frac{k^{2}}{2},\) then

1. a = 0, k = 8
2. 4a – k + 8 = 0
3. det (P adj (Q)) = 2⁹
4. det (Q adj(P)) = 2¹³