#### Please solve RD Sharma solution for Maths Class 12 Chapter 5 Determinants Exercise Very short question Question 11 for maths textbook solution.

Answer: $0$

Hint: Here we use basic concept of determinant of matrix

Given: $\Delta=\left|\begin{array}{ccc} 1 & \omega & \omega^{2} \\ \omega & \omega^{2} & 1 \\ \omega^{2} & 1 & \omega \end{array}\right|$

Solution :

$C_{1} \rightarrow C_{1}+C_{2}+C_{3}$

So,

$\Delta=\left|\begin{array}{ccc} 1+\omega+\omega^{2} & \omega & \omega^{2} \\ 1+\omega+\omega^{2} & \omega^{2} & 1 \\ 1+\omega+\omega^{2} & 1 & \omega \end{array}\right|$

$\rightarrow$ We know that  $1+\omega+\omega^{2}=0$

So,

$\Delta=\left|\begin{array}{ccc} 0 & \omega & \omega^{2} \\ 0 & \omega^{2} & 1 \\ 0 & 1 & \omega \end{array}\right|$

$\rightarrow$ Here whole 1st column is zero

So, the value of determinant is also zero