Let P = [(3,-1,-2),(2,0,α),(3,-5,0)], where α ∈ ℝ .

Question

Let P = \(\begin{bmatrix} 3 & -1 & -2 \\ 2 & 0 & α \\ 3 & -5 & 0 \end{bmatrix}\) , 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 q₂₃ = -k/8 and det (Q) = \(\frac{k^2}{2}\) , then

(A) α = 0 , k = 8

(B) 4α - k + 8 = 0

(C) det(P adj(Q)) = 2⁹

(D) det(Q adj(P)) = 2¹³

Answer 1

(B) 4α - k + 8 = 0

(C) det(P adj(Q)) = 2⁹