Transpose of a Matrix

Find the order of transpose of matrix $A$ with order $3\times 4$.

Find the order of transpose of matrix $A$ with order $1\times 3$.

If $A=\left[\begin{array}{ll}2& 3\\ -1& 4\end{array}\right]$ and $B=\left[\begin{array}{cc}1& -1\\ 2& 5\end{array}\right]$ then value of ${\left(AB\right)}^T$ and $B^T{A}^T$ is

What is the transpose of the matrix $\left[\begin{array}{cc}0& 2\\ -2& 4\end{array}\right]$?

The order of matrix $A$ is $3\times 4$ and $B$ is a matrix such that $A^{T}B$ and $A{B}^T$ both are defined then find the order of $B$.

Let $\mathrm{A}$ and $\mathrm{B}$ be $3\times 3$ symmetric matrices such that $\mathrm{X}=\mathrm{AB}+\mathrm{BA}$ and $\mathrm{Y}=\mathrm{AB}-\mathrm{BA},$ then the value of $(\mathrm{XY}{)}^{\mathrm{T}}$ is, where $(\mathrm{XY}{)}^{\mathrm{T}}$ is the transpose of the matrix $\mathrm{XY}$.

$P$ is a $3\times 3$ matrix such that $P^{\top }=3P+2I$, where $P^{\top }$ is the transpose of $P$ and $l$ is the identity matrix. If $X$ is a column matrix satisfying $X=\left[\begin{array}{l}x\\ y\\ z\end{array}\right]=\left[\begin{array}{l}0\\ 0\\ 0\end{array}\right]$, then

If $\mathrm{A}\mathrm{ }\mathrm{a}\mathrm{n}\mathrm{d}\mathrm{ }\mathrm{B}$ are symmetric matrices, then $\mathrm{A}\mathrm{B}-\mathrm{B}\mathrm{A}$ is a

Suppose $A \text{and} B$ are two square matrices of same order. If $A, B$ are symmetric matrices, then $AB - BA$ is

If $A=\frac{1}{9} \left[\begin{array}{ccc}-8& 1& 4\\ 4& 4& 7\\ 1& -8& 4\end{array}\right]$ then $A$ is -

If matrix $A=\left[\begin{array}{ccc}a& b& c\\ b& c& a\\ c& a& b\end{array}\right],$ where a.b. c are real positive number , $abc = 1$ and $A^{T}A=I,$ then which of the following is-are true.

If $\mathrm{A}=\left[\mathrm{ }\begin{array}{lll}0& –1& 2\\ 1& 0& 3\\ –2& –3& 0\end{array}\mathrm{ }\right]$ . Then $\mathrm{A}+2{\mathrm{A}}^{\mathrm{T}}$ equals to

Let matrix $A=\left[ \begin{array}{lll}a& b& c\\ b& c& a\\ c& a& b\end{array} \right]$, where $a,b,c$ are real positive numbers with $abc=1$. if $A^{T}A=I$ , then the value of $a^3+ b^3+ c^3$ is equal to

Let matrix $\mathrm{A}=\left[\begin{array}{lll}\mathrm{a}& \mathrm{b}& \mathrm{c}\\ \mathrm{b}& \mathrm{c}& \mathrm{a}\\ \mathrm{c}& \mathrm{a}& \mathrm{b}\end{array}\right]$ where $\mathrm{a},\mathrm{ }\mathrm{b},\mathrm{ }\mathrm{c}$ are real positive numbers with $\mathrm{a}\mathrm{b}\mathrm{c}=1. \text{If} {\mathrm{A}}^{\mathrm{T}}\mathrm{A}=\mathrm{I}$ , then ${\mathrm{a}}^3+\mathrm{ }{\mathrm{b}}^3+\mathrm{ }{\mathrm{c}}^3=$

Let a matrix $A=\left[\begin{array}{ll}1& 1\\ 0& 1\end{array}\right],\mathrm{ }P=\left[\begin{array}{ll}\frac{\sqrt{3}}{2}& \frac{1}{2}\\ -\frac{1}{2}& \frac{\sqrt{3}}{2}\end{array}\right]$ , $\mathrm{ }Q=PA{P}^T$ where $P^T$ is transpose of matrix $P$ . then $P^T{Q}^{2005}P$ is

If $\mathrm{A}$ is a $3\times 3$ skew-symmetric matrix, then $\left|\mathrm{A}\right|$ is given by -

For a given matrix $\mathrm{A}=\left[\begin{array}{ll}\cos \mathrm{\theta }& -\sin \mathrm{\theta }\\ \sin \mathrm{\theta }& \cos \mathrm{\theta }\end{array}\right]$ which of the following statement holds good:

If $\mathrm{A}=\frac{1}{9}\left[\begin{array}{lll}-8& 1& 4\\ 4& 4& 7\\ 1& -8& 4\end{array}\right]$ then A is -