Let $A = \begin{bmatrix} 0 & 0 & 1 \\ 1 & 0 & 0 \\ 0 & 0 & 0 \end{bmatrix}$, $B = \begin{bmatrix} 0 & 1 & 0 \\ 0 & 0 & 1 \\ 0 & 0 & 0 \end{bmatrix}$, and $P = \begin{bmatrix} 0 & 1 & 0 \\ x & 0 & 0 \\ 0 & 0 & y \end{bmatrix}$ be an orthogonal matrix such that $B = PAP^{-1}$ holds. Then:
- A$x = 1, y = 1$
- B$x = 1, y = 0$
- C$x = 0, y = 1$
- D$x = -1, y = 0$
Explore More
Similar Questions
Suppose $\det \begin{bmatrix} \sum_{k=0}^n k & \sum_{k=0}^n {^nC_k} k^2 \\ \sum_{k=0}^n {^nC_k} k & \sum_{k=0}^n {^nC_k} 3^k \end{bmatrix} = 0$ holds for some positive integer $n$. Then $\sum_{k=0}^n \frac{{^nC_k}}{k+1}$ equals
DifficultIIT 2019
View SolutionFor any $3 \times 3$ matrix $M$,let $|M|$ denote the determinant of $M$. Let $I$ be the $3 \times 3$ identity matrix. Let $E$ and $F$ be two $3 \times 3$ matrices such that $(I-EF)$ is invertible. If $G=(I-EF)^{-1}$,then which of the following statements is (are) $TRUE$?
$(A) |FE|=|I-FE||FGE|$
$(B) |I-FE|(I+FGE)=I$
$(C) EFG=GEF$
$(D) (I-FE)(I-FGE)=I$
$(A) |FE|=|I-FE||FGE|$
$(B) |I-FE|(I+FGE)=I$
$(C) EFG=GEF$
$(D) (I-FE)(I-FGE)=I$
If $\omega$ is a root of the equation $x+\frac{1}{x}+1=0$,then the value of the determinant $\left|\begin{array}{ccc}1 & 1+\omega & 1+\omega+\omega^2 \\ 3 & 4+3 \omega & 5+4 \omega+3 \omega^2 \\ 6 & 9+6 \omega & 11+9 \omega+6 \omega^2\end{array}\right|$ is equal to
DifficultAP EAMCET 2021
View SolutionMatch List-$I$ with List-$II$:
List-$I$ List-$II$ a) $A$ matrix which is not a square matrix i) Symmetric matrix b) $A$ square matrix $A' = A$ ii) Null matrix c) The diagonal elements of a diagonal matrix are same iii) Rectangular matrix d) $A$ matrix which is both symmetric and skew symmetric iv) Scalar matrix
| List-$I$ | List-$II$ |
| a) $A$ matrix which is not a square matrix | i) Symmetric matrix |
| b) $A$ square matrix $A' = A$ | ii) Null matrix |
| c) The diagonal elements of a diagonal matrix are same | iii) Rectangular matrix |
| d) $A$ matrix which is both symmetric and skew symmetric | iv) Scalar matrix |
MediumKCET 2026
View SolutionLet $A$ and $B$ be any two $n \times n$ matrices such that the following conditions hold: $A B=B A$ and there exist positive integers $k$ and $l$ such that $A^k=I$ (the identity matrix) and $B^l=0$ (the zero matrix). Then,
Vedclass Products
For Students
Vedclass Test Series
Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.
Start Free TrialFor Teachers
Exam Paper Generator
Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.
Try FreeFor Institutes
Online Exam Module
Live online exams with unlimited students, 360° analytics & white-label branding.
See Demo