Question:
Value of the determinant \[\begin{vmatrix}1 & w & w^2 \\w & w^2 & 1 \\w^2 & 1 & w\end{vmatrix}\] where \( w \) is the cube root of unity is:
Value of the determinant \[\begin{vmatrix}1 & w & w^2 \\w & w^2 & 1 \\w^2 & 1 & w\end{vmatrix}\] where \( w \) is the cube root of unity is:
Updated On: Jul 12, 2024
- 1
- 0
- \( w \)
- \( w^2 \)
Hide Solution
Verified By Collegedunia
The Correct Option is B
Solution and Explanation
The correct option is (B): 0
Was this answer helpful?
0
0
Top Questions on Matrices
- For the matrices \( A = \begin{bmatrix} 3 & -4 \\ 1 & -1 \end{bmatrix} \) and \( B = \begin{bmatrix} -29 & 49 \\ -13 & 18 \end{bmatrix} \), if \( (A^{15} + B) \begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} 0\\ 0 \end{bmatrix} \), then among the following which one is true?}
- For the matrix $A=\begin{bmatrix}5 & 0 \\ 0 & 5\end{bmatrix}$, the value of $|\text{adj}\,A|$ is
- A matrix has 13 elements. The number of possible different orders it can have is
If A and B are two n times n non-singular matrices, then
- The number of $3\times2$ matrices $A$, which can be formed using the elements of the set $\{-2,-1,0,1,2\}$ such that the sum of all the diagonal elements of $A^{T}A$ is $5$, is
View More Questions
Questions Asked in NATA exam
- How many numbers are divisible by 3 between 50 and 500?
- NATA - 2025
- Calculus
Which of the following is a sedimentary rock?
- NATA - 2025
- Environmental Chemistry
- The ratio of ages of Rahul and Neha is 3:4. After 5 years, the ratio becomes 4:5. What are their current ages?
- NATA - 2025
- Algebra
Mantri Mandir -- Where is it located?
- NATA - 2025
- Architectural Knowledge
Count the no of surfaces
- NATA - 2025
- Architectural Knowledge
View More Questions