WBJEE · Maths · Sets and Relations
We define a binary relation - on the set of all \(3 \times 3\) real matrices as \(A \sim B,\) if and only if there exist invertible matrices \(P\) and \(Q\) such that \(B=P A Q^{-1} .\) The binary relation \(\sim\) is
- A neither reflexive nor symmetric
- B reflexive and symmetric but not transitive
- C symmetric and transitive but not reflexive
- D an equivalence relation
Answer & Solution
Correct Answer
(D) an equivalence relation
Step-by-step Solution
Detailed explanation
Let the relation defined as \(R=\left\{(A, B): B=P A Q^{-1}\right\}\) For reflexive \(A=I A I^{-1}\) \(\Rightarrow(A, A) \in R\) \(\Rightarrow R\) is reflexive For symmetric \(\operatorname{Let}(A, B) \in R\) \(\therefore B=P A Q^{-1}\)…
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Maths
- Let \(y=e^{x^{2}}\) and \(y=e^{x^{2}} \sin x\) be two given curves. Then, angle between the tangents to the curves at any point of their intersectionWBJEE 2015 Medium
- The value of \(\lim _{n \rightarrow \infty}\left\{\frac{\sqrt{n+1}+\sqrt{n+2}+\ldots+\sqrt{2 n-1}}{n^{3 / 2}}\right\}\) isWBJEE 2016 Medium
- If \(R\) be the set of all real numbers and \(f: R \rightarrow R\) is given by \(f(x)=3 x^{2}+1\). Then, the set \(f^{-1}([1,6])\) isWBJEE 2014 Medium
- Let \(z_1\) and \(z_2\) be two non-zero complex numbers. ThenWBJEE 2022 Easy
- For \(0 \leq P, Q \leq \frac{\pi}{2},\) if \(\sin P+\cos Q=2\), then the
value of \(\tan \left(\frac{\vec{P}+Q}{2}\right)\) is equal toWBJEE 2013 Medium - S and \(T\) are the foci of an ellipse and B is end point of the minor axis. If STB is an equilateral triangle, the eccentricity of the ellipse isWBJEE 2010 Medium
More PYQs from WBJEE
- An electron in a circular orbit of radius \(0.05 \mathrm{nm}\) performs \(10^{16}\) revolutions per second. The maghetic moment due to this rotation of electron is (in \(\mathrm{Am}^{2}\) )WBJEE 2014 Easy
- The correct order of \(\mathrm{O}-\mathrm{O}\) bond length in \(\mathrm{O}_{2}, \mathrm{H}_{2} \mathrm{O}_{2}\) and \(\mathrm{O}_{3}\) isWBJEE 2016 Medium
- Let \(f(x)\) be continuous on \([0,5]\) and differentiable in \((0,5)\). If \(f(0)=0\) and \(\left|f^{\prime}(x)\right| \leq \frac{1}{5}\) for all \(x\) in \((0,5)\), then \(\forall x\) in \([0,5]\).WBJEE 2025 Medium
- \(\lim _{n \rightarrow \infty} \frac{\sqrt{n}}{\sqrt{\left(n^{3}\right)}}+\frac{\sqrt{n}}{\sqrt{(n+4)^{3}}}+\frac{\sqrt{n}}{\sqrt{(n+8)^{3}}}+\cdots \cdots \cdots+\frac{\sqrt{n}}{\sqrt{[n+4(n-1)]^{3}}}\) isWBJEE 2021 Hard
- A charged particle moves with constant velocity in a region where no effect of gravity is felt but an electrostatic field \(\overrightarrow{\mathrm{E}}\)
together with a magnetic field \(\vec{B}\) may be present. Then which of the following cases are possible?WBJEE 2020 Easy - The integrating factor of the differential equation \(\frac{d y}{d x}+\left(3 x^{2} \tan ^{-1} y -x^{3}\right)\left(1+y^{2}\right)=0\) isWBJEE 2015 Medium