(B) matrix $A$ is orthogonal if $A^T A = I$. Taking the determinant on both sides, we get $|A^T A| = |I|$. Since $|A^T| = |A|$, we have $|A|^2 = 1$, w

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

(B) matrix $A$ is orthogonal if $A^T A = I$. Taking the determinant on both sides, we get $|A^T A| = |I|$. Since $|A^T| = |A|$, we have $|A|^2 = 1$, which implies $|A| = \pm 1$. Since $|A| \neq 0$, every orthogonal matrix is non-singular. Thus, $Q \subseteq P$. Since there exist non-singular matrices that are not orthogonal (e.g.,any diagonal matrix with entries other than $1$ or $-1$), $Q$ is a proper subset of $P$.

Class 12 Mathematics 3 and 4 .Determinants and Matrices Types of matrices, Algebra of matrices

Easy

Let $P$ be the set of all non-singular matrices of order $3$ over $\mathbb{R}$ and $Q$ be the set of all orthogonal matrices of order $3$ over $\mathbb{R}$. Then,

WBJEE 2017 All WBJEE

A
$P$ is a proper subset of $Q$
B
$Q$ is a proper subset of $P$
C
Neither $P$ is a proper subset of $Q$ nor $Q$ is a proper subset of $P$
D
$P \cap Q = \phi$, the void set

Explore More

Browse All

Question Bank

All Subjects

Class 12 Questions

Class 12

Mathematics Questions

Chapter

3 and 4 .Determinants and Matrices

Subtopic

Types of matrices, Algebra of matrices

Previous Year

WBJEE 2017 Paper All WBJEE years →

Construct a $2 \times 2$ matrix,$A = [a_{ij}]$,whose elements are given by $a_{ij} = \frac{i}{j}$.

Medium

View Solution

If $A = \begin{bmatrix} 3 & 4 \\ 1 & -6 \end{bmatrix}$ and $B = \begin{bmatrix} -2 & 5 \\ 6 & 1 \end{bmatrix}$,then find $X$ such that $A + 2X = B$.

Difficult

View Solution

Given $A = \begin{bmatrix} \sqrt{3} & 1 & -1 \\ 2 & 3 & 0 \end{bmatrix}$ and $B = \begin{bmatrix} 2 & \sqrt{5} & 1 \\ -2 & 3 & \frac{1}{2} \end{bmatrix}$,find $A + B = \dots \dots \dots$

Easy

View Solution

If matrix $A = \begin{bmatrix} 1 & 3k + \frac{1}{3} \\ 0 & 1 \end{bmatrix}$,then the value of $\prod_{k=1}^{36} \begin{bmatrix} 1 & 3k + \frac{1}{3} \\ 0 & 1 \end{bmatrix}$ is equal to :-

View Solution

If $A = \begin{bmatrix} -1 & 0 \\ 0 & 2 \end{bmatrix}$, then $A^3 - A^2$ is equal to

MediumTS EAMCET 2005

View Solution

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial

For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free

For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo

Let $P$ be the set of all non-singular matrices of order $3$ over $\mathbb{R}$ and $Q$ be the set of all orthogonal matrices of order $3$ over $\mathbb{R}$. Then,

Similar Questions

Construct a $2 \times 2$ matrix,$A = [a_{ij}]$,whose elements are given by $a_{ij} = \frac{i}{j}$.

If $A = \begin{bmatrix} 3 & 4 \\ 1 & -6 \end{bmatrix}$ and $B = \begin{bmatrix} -2 & 5 \\ 6 & 1 \end{bmatrix}$,then find $X$ such that $A + 2X = B$.

Given $A = \begin{bmatrix} \sqrt{3} & 1 & -1 \\ 2 & 3 & 0 \end{bmatrix}$ and $B = \begin{bmatrix} 2 & \sqrt{5} & 1 \\ -2 & 3 & \frac{1}{2} \end{bmatrix}$,find $A + B = \dots \dots \dots$

If matrix $A = \begin{bmatrix} 1 & 3k + \frac{1}{3} \\ 0 & 1 \end{bmatrix}$,then the value of $\prod_{k=1}^{36} \begin{bmatrix} 1 & 3k + \frac{1}{3} \\ 0 & 1 \end{bmatrix}$ is equal to :-

If $A = \begin{bmatrix} -1 & 0 \\ 0 & 2 \end{bmatrix}$, then $A^3 - A^2$ is equal to

Vedclass Test Series

Exam Paper Generator

Online Exam Module