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NDA 2022
Exam
NDA
Year
2022
Subject
Mathematics
Chapter
Matrices

NDA 2022 · Mathematics · Matrices

If A=[ array ccc 2 θ & θ & 0 -2 θ & θ & 0 -1 & 1 & 1 array ] , then...

If A=\left[2sin⁡θcos⁡θ0−2cos⁡θsin⁡θ0−111\begin{array}{ccc}2 \sin \theta & \cos \theta & 0 \\ -2 \cos \theta & \sin \theta & 0 \\ -1 & 1 & 1\end{array}\right], then what is A(adj⁡A)A(\operatorname{adj} A) equal to? where II is the identify matrix.

Options

  1. ANullmatrix
  2. B−I-I
  3. CII
  4. D2I2I

Correct answer

D. 2I2I

Step-by-step solution

|A|=\left|2sin⁡θcos⁡θ0−2cos⁡θsin⁡θ0−111\begin{array}{ccc}2 \sin \theta & \cos \theta & 0 \\ -2 \cos \theta & \sin \theta & 0 \\ -1 & 1 & 1\end{array}\right|=2 We know that A(adj⁡A)=∣A∣I=2IA(\operatorname{adj} A)=|A| I=2 I
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