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WBJEE · Maths · Matrices

If \(\operatorname{adj} \mathrm{B}=\mathrm{A},|\mathrm{P}|=|\mathrm{Q}|=1\), then \(\operatorname{adj}\left(\mathrm{Q}^{-1} \mathrm{BP}^{-1}\right)=\)

  1. A PQ
  2. B QAP
  3. C PAQ
  4. D \(\mathrm{PA}^{-1} \mathrm{Q}\)
Verified Solution

Answer & Solution

Correct Answer

(C) PAQ

Step-by-step Solution

Detailed explanation

\begin{aligned} & \left.\text { adj( } Q^{-1} B P^{-1}\right) \\ & =\left|Q^{-1} B P^{-1}\right|\left(Q^{-1} B P^{-1}\right)^{-1} \\ & =\left|Q^{-1}\right||B|\left|P^{-1}\right| PB^{-1} Q \\ & =|B| P \frac{(\operatorname{adj} \mathrm{~B})}{|B|} Q \\ & =\text { PAQ }\end{aligned}