Class 12Mathematics3-4. Matrices and DeterminantsSpecial types of matrices, Transpose of matrices and Trace of matrices
MediumIf $A$ is a skew-symmetric matrix,then (given $n \in N$):
$1$. $A^{2n}$ is a skew-symmetric matrix.
$2$. $A^{2n+1}$ is a skew-symmetric matrix.
$1$. $A^{2n}$ is a skew-symmetric matrix.
$2$. $A^{2n+1}$ is a skew-symmetric matrix.
- A$1$ is true,$2$ is false
- BBoth $1$ and $2$ are true
- CBoth $1$ and $2$ are false
- D$1$ is false,$2$ is true
Explore More
Similar Questions
If a square matrix $A$ is such that $\left(A^T-\frac{1}{2} I\right)\left(A-\frac{1}{2} I\right) = \left(A^T+\frac{1}{2} I\right)\left(A+\frac{1}{2} I\right) = I$,where $I$ is a unit matrix,then $A$ is
If $A=\left[\begin{array}{rrr}-1 & 2 & 3 \\ 5 & 7 & 9 \\ -2 & 1 & 1\end{array}\right]$ and $B=\left[\begin{array}{rrr}-4 & 1 & -5 \\ 1 & 2 & 0 \\ 1 & 3 & 1\end{array}\right],$ then verify that $(A-B)^{\prime}=A^{\prime}-B^{\prime}$.
Easy
View SolutionIf $A$ and $B$ are skew-symmetric matrices of the same order,then $(AB)^{\prime} =$ . . . . . . .
$P$ is an orthogonal matrix and $A$ is a periodic matrix with period $4$,and $Q = PAP^T$. Then $X = P^TQ^{2005}P$ will be equal to
Difficult
View SolutionFor the matrix $A = \begin{bmatrix} 1 & 5 \\ 6 & 7 \end{bmatrix}$,verify that $(A + A^{\prime})$ is a symmetric matrix.
Easy
View SolutionVedclass 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