Let P= [p_ i j ] and Q= [q_ i j ] be two square matrices of order 3 such that q_ ij =2^ ( i + j -1) p _ ij and det ( Q )=2¹⁰ . Then the value of det ( adj ( adj P )) is:

Step-by-step solution

vmatrix 2p₁₁ & 2^2p₁₂ & 2^3p₁₃ 2^2p₂₁ & 2^3p₂₂ & 2^4p₂₃ 2^3p₃₁ & 2^4p₃₂ & 2^5p₃₃ vmatrix = 2¹⁰ 2^2 2 2^3 vmatrix p₁₁ & p₁₂ & p₁₃ 2p₂₁ & 2p₂₂ & 2p₂₃ 2^2p₃₁ & 2^2p₃₂ & 2^2p₃₃ vmatrix = 2¹⁰ 2^9 vmatrix p₁₁ & p₁₂ & p₁₃ p₂₁ & p₂₂ & p₂₃ p₃₁ & p₃₂ & p₃₃ vmatrix = 2¹⁰ |P| = 2 | adj ( adj (P))| = |P|^ (n-1)^2 = |P|^4 = 2^4 = 16