ExamBro
ExamBro
AP EAMCET · Maths · Matrices

If \(P\) and \(Q\) are two \(3 \times 3\) matrices such that \(|P Q|=1\) and \(|P|=9\), then the determinant of adjoint the matrix \(P\). Adj \(3 Q\) is

  1. A \(9^4\)
  2. B \(\frac{1}{9^4}\)
  3. C \(9^2\)
  4. D \(\frac{1}{9^2}\)
Verified Solution

Answer & Solution

Correct Answer

(A) \(9^4\)

Step-by-step Solution

Detailed explanation

\begin{aligned} & |P||Q|=1 \Rightarrow|Q|=\frac{1}{9} \\ & \Rightarrow \mid \operatorname{adj}(P \operatorname{adj}(3 Q)|=|\operatorname{adj} \operatorname{adj}(3 Q)|| \operatorname{adj} P \mid \\ & =|3 Q|^4|P|^2=\left(3^3\right)^4 \times|Q|^4|P|^2 \\ & =3^{12} \times…