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AP EAMCET · Maths · Matrices

Let \(A\) be a \(4 \times 4\) matrix and \(P\) be its adjoint matrix. If \(|P|=\left|\frac{A}{2}\right|\), then \(\left|A^{-1}\right|=\)

  1. A \(\pm \frac{1}{4}\)
  2. B \(\pm 8\)
  3. C \(\pm 2\)
  4. D \(\pm 4\)
Verified Solution

Answer & Solution

Correct Answer

(D) \(\pm 4\)

Step-by-step Solution

Detailed explanation

\begin{aligned} & \text { } \mathrm{P}=\operatorname{adj}(\mathrm{A}) \\ & |\mathrm{P}|=|\operatorname{adj}(\mathrm{A})|=|\mathrm{A}|^{n-1}=|\mathrm{A}|^3 \\ & |\mathrm{P}|=\left|\frac{\mathrm{A}}{2}\right|=\frac{1}{2^4}|\mathrm{~A}| \\ &…