JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
Let \(A\) and \(B\) be any two \(3\times3\) matrices. If \(A\) is symmetric and \(B\) is skewsymmetric, then the matrix \(AB - BA\) is
- A skewsymmetric
- B symmetric
- C neither symmetric nor skewsymmetric
- D \(I\) or \(-I\), where \(I\) is an identity matrix
Answer & Solution
Correct Answer
(B) symmetric
Step-by-step Solution
Detailed explanation
Let \(A\) be symmetric matrix and \(B\) be skew symmetric matrix. \(\therefore {A^T} = A\) and \({B^T} = - B\) Consider \({\left( {AB - BA} \right)^T} = \left( {A{B^T}} \right) - {\left( {BA} \right)^T}\) \( = {B^T}{A^T} - {A^T}{B^T}\)…
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 \(\vec{a}=\hat{i}+\alpha \hat{j}+3 \hat{k}\) and \(\vec{b}=3 \hat{i}-\alpha \hat{j}+\hat{k} \cdot\) If the area of the parallelogram whose adjacent sides are represented by the vectors \(\vec{a}\) and \(\vec{b}\) is \(8 \sqrt{3}\) square units, then \(\overrightarrow{ a } \cdot \overrightarrow{ b }\) is equal to ....... .JEE Mains 2021 Medium
- Let \(y=y(x)\) be the solution of the differential equation \(\frac{d y}{d x}+\frac{2 x}{\left(1+x^2\right)^2} y=x e^{\frac{1}{\left(1+x^2\right)}} ; y(0)=0\). Then the area enclosed by the curve \(f(\mathrm{x})=\mathrm{y}(\mathrm{x}) \mathrm{e}^{-\frac{1}{\left(1+\mathrm{x}^2\right)}}\) and the line \(\mathrm{y}-\mathrm{x}=4\) is ...........JEE Mains 2024 Hard
- Let \(I(x)=\int \frac{6}{\sin ^2 x(1-\cot x)^2} d x\). If \(I(0)=3\), then \(\mathrm{I}\left(\frac{\pi}{12}\right)\) is equal to :JEE Mains 2024 Hard
- For some \(\theta\in(0,\frac{\pi}{2}),\) let the eccentricity and the length of the latus rectum of the hyperbola \(x^{2}-y^{2}sec^{2}\theta=8\) be \(e_{1}\) and \(l_{1}\), respectively, and let the eccentricity and the length of the latus rectum of the ellipse \(x^{2}sec^{2}\theta+y^{2}=6\) be \(e_{2}\) and \(l_{2},\) respectively. If \(e_{1}^{2}=e_{2}^{2}(sec^{2}\theta+1)\), then \((\frac{l_{1}l_{2}}{e_{1}e_{2}})tan^{2}\theta\) is equal to ___ .JEE Mains 2026 Medium
- If \({\left( {10} \right)^9} + 2{\left( {11} \right)^1}{\left( {10} \right)^8} + 3{\left( {11} \right)^2}{\left( {10} \right)^7} + ..\;.\;.\;.\; + 10\left( {{{11}^9}} \right) = \;k{\left( {10} \right)^9}\) ,then \(k \) is equal toJEE Mains 2014 Hard
- Let \(\vec{a}=\hat{i}+2 \hat{j}+3 \hat{k}, \vec{b}=3 \hat{i}+\hat{j}-\hat{k}\) and \(\vec{c}\) be three vectors such that \(\vec{c}\) is coplanar with \(\vec{a}\) and \(\vec{b}\). If the vector \(\vec{C}\) is perpendicular to \(\vec{b}\) and \(\vec{a} \cdot \vec{c}=5\), then \(|\vec{c}|\) is equal toJEE Mains 2025 Medium
More PYQs from JEE Mains
- If \(\sum_{r=1}^{13}\left\{\frac{1}{\sin \left(\frac{\pi}{4}+(r-1) \frac{\pi}{6}\right) \sin \left(\frac{\pi}{4}+\frac{r \pi}{6}\right)}\right\}=a \sqrt{3}+b, a, b \in \mathbf{Z}\), then \(a^2+b^2\) is equal to :JEE Mains 2025 Hard
- Let \(f:R \to R\) be a continuously differentiable function such that \(f\left( 2 \right) = 6\) and \(f'\left( 2 \right) = \frac{1}{{48}}\). If \(\int_6^{f\left( x \right)} {4{t^3}} \,dt = \left( {x - 2} \right)\,g\left( x \right)\), then \(\mathop {\lim }\limits_{x \to 2} \,g\left( x \right)\) is equal toJEE Mains 2019 Hard
- Let \((\alpha, \beta, \gamma)\) be the image of the point \(P (2,3,5)\) in the plane \(2 x + y -3 z =6\). Then \(\alpha+\beta+\gamma\) is equal toJEE Mains 2023 Medium
- For \(n \in N\), if \(\cot ^{-1} 3+\cot ^{-1} 4+\cot ^{-1} 5+\cot ^1 n=\frac{\pi}{4}\), then \(\mathrm{n}\) is equal to .........JEE Mains 2024 Medium
- For \(\alpha, \beta \in\left(0, \frac{\pi}{2}\right)\), let \(3 \sin (\alpha+\beta)=2 \sin (\alpha-\beta)\) and a real number \(k\) be such that \(\tan \alpha=k \tan \beta\). Then the value of \(\mathrm{k}\) is equal to :JEE Mains 2024 Hard
- The sum of an infinite geometric series with positive terms is \(3\) and the sum of the cubes of its terms is \(\frac {27}{19}\). Then the common ratio of this series isJEE Mains 2019 Hard