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NDA 2015
Exam
NDA
Year
2015
Subject
Mathematics
Chapter
Matrices

NDA 2015 · Mathematics · Matrices

If A is an orthogonal matrix of order 3 and B=[ array ccc 1 & 2 & 3...

If AA is an orthogonal matrix of order 3 and B=\left[123−302250\begin{array}{ccc}1 & 2 & 3 \\ -3 & 0 & 2 \\ 2 & 5 & 0\end{array}\right], then which of the following is/are correct? 1. ∣AB∣=±472.AB=BA|\mathrm{AB}|= \pm 47 2. \mathrm{AB}=\mathrm{BA} Select the correct answer using the code given below :

Options

  1. A1 only
  2. B2 only
  3. CBoth 1 and 2
  4. DNeither 1 nor 2

Correct answer

A. 1 only

Step-by-step solution

The determinent of aorthogonalmatrixisalways±1a orthogonal matrix is always \pm 1∣A∣=±1B=[123−302250]∣B∣=−10−2(−4)+3(−15)=−47∣AB∣=∣A∣∣B∣=(±1)(−47)=±47\begin{aligned} & |\mathrm{A}|= \pm 1 \\ & \mathrm{ B}=\left[\begin{array}{ccc} 1 & 2 & 3 \\ -3 & 0 & 2 \\ 2 & 5 & 0 \end{array}\right] \\ & |\mathrm{B}|=-10-2(-4)+3(-15) \\ & =-47 \\ & |\mathrm{AB}|=|\mathrm{A}||\mathrm{B}| \\ & =( \pm 1)(-47) \\ & = \pm 47 \end{aligned}$
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