#### Need Solution for R.D. Sharma Maths Class 12 Chapter 4 Algebra of Matrices Exercise Multiple Choice Questions Question 24 Maths Textbook Solution.

Answer: The correct option is $\text { (C), } \theta=2 n \pi+\frac{\pi}{3}, n \in Z$

Given:$A=\left[\begin{array}{cc} \cos \theta & -\sin \theta \\ \sin \theta & \cos \theta \end{array}\right]$

Solution:

Now,

$A=\left[\begin{array}{cc} \cos \theta & -\sin \theta \\ \sin \theta & \cos \theta \end{array}\right]$

\begin{aligned} &\Rightarrow A^{T}=\left[\begin{array}{cc} \cos \theta & \sin \theta \\ -\sin \theta & \cos \theta \end{array}\right] \\ &A+A^{T}=\left[\begin{array}{cc} \cos \theta & -\sin \theta \\ \sin \theta & \cos \theta \end{array}\right]+\left[\begin{array}{cc} \cos \theta & \sin \theta \\ -\sin \theta & \cos \theta \end{array}\right]=\left[\begin{array}{cc} 1 & 0 \\ 0 & 1 \end{array}\right] \\ &\Rightarrow 2 \cos \theta=1 \\ &\cos \theta=\frac{1}{2} \\ &\Rightarrow \theta=2 n \pi+\frac{\pi}{3}\{n \in Z\} \end{aligned}

So, the correct option is (C).