Class 12Mathematics3-4. Matrices and DeterminantsSpecial types of matrices, Transpose of matrices and Trace of matrices
EasyFind the transpose of the following matrix: $\left[\begin{array}{cc}1 & -1 \\ 2 & 3\end{array}\right]$
- A$\left[\begin{array}{cc}1 & 2 \\ -1 & 3\end{array}\right]$
- B$\left[\begin{array}{cc}1 & -1 \\ 2 & 3\end{array}\right]$
- C$\left[\begin{array}{cc}2 & 3 \\ 1 & -1\end{array}\right]$
- D$\left[\begin{array}{cc}-1 & 1 \\ 3 & 2\end{array}\right]$
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Similar Questions
For the matrix $A = \begin{bmatrix} 1 & 5 \\ 6 & 7 \end{bmatrix}$,verify that $(A + A^{\prime})$ is a symmetric matrix.
Easy
View SolutionExpress the matrix $A = \left[\begin{array}{cc}1 & 5 \\ -1 & 2\end{array}\right]$ as the sum of a symmetric and a skew-symmetric matrix.
Easy
View SolutionIf 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
For any square matrix $A$,$AA^T$ is a
Medium
View SolutionIf $A$ 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.
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