Let the function
Question:

Let $A=\left(\begin{array}{ccc}0 & 2 q & r \\ p & q & -r \\ p & -q & r\end{array}\right)$. It AAT $A^{T} I_{3}$, then $|p|$ is :

  1. $\frac{1}{\sqrt{2}}$

  2. $\frac{1}{\sqrt{5}}$

  3. $\frac{1}{\sqrt{6}}$

  4. $\frac{1}{\sqrt{3}}$


Correct Option: 1

Solution:

A is orthogonal matrix

$\Rightarrow 0^{2}+\mathrm{p}^{2}+\mathrm{p}^{2}=1 \Rightarrow|\mathrm{p}|=\frac{1}{\sqrt{2}}$

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