Transpose of a Matrix

If $A=\left[\begin{array}{lll}-1& 2& 3\\ 5& 7& 9\\ -2& 1& 1\end{array}\right]$ and $B=\left[\begin{array}{ccc}-4& 1& -5\\ 1& 2& 0\\ 1& 3& 1\end{array}\right]$, then verify that $(A+B{)}^{\text{'}}=A^{\text{'}}+B^{\text{'}}$

Find the transpose:

$\left[\begin{array}{ccc}-1& 5& 6\\ \sqrt{3}& 5& 6\\ 2& 3& -1\end{array}\right]$

Find the transpose:

$\left[\begin{array}{cc}1& -1\\ 2& 3\end{array}\right]$

If $A=\left[\begin{array}{cc}\cos \alpha & -\sin \alpha \\ \sin \alpha & \cos \alpha \end{array}\right]$, and $A+A^{\text{'}}=I$, then the value of $\alpha$ is

Find $\frac{1}{2}\left(A+A^{\text{'}}\right)$ and  $\frac{1}{2}\left(A-A^{\text{'}}\right)$, when $A=\left[\begin{array}{ccc}0& a& b\\ -a& 0& c\\ -b& -c& 0\end{array}\right]$

If $A=\left[\begin{array}{ll}\sin \alpha & \cos \alpha \\ -\cos \alpha & \sin \alpha \end{array}\right]$ , then verify that  $A^{\text{'}}A=I$

 If $A=\left[\begin{array}{ll}\cos \alpha & \sin \alpha \\ -\sin \alpha & \cos \alpha \end{array}\right]$ , then verify that $A^{\text{'}}A=I$

For the matrices $A$ and $B$ verify that $(AB{)}^{\text{'}}=B^{\text{'}}{A}^{\text{'}}.$ where
$A=\left[\begin{array}{l}0\\ 1\\ 2\end{array}\right],B=\left[\begin{array}{lll}1& 5& 7\end{array}\right]$

For the matrices $A$ and $B$ verify that $(AB{)}^{\text{'}}=B^{\text{'}}{A}^{\text{'}},$ where
$A=\left[\begin{array}{l}1\\ -4\\ 3\end{array}\right],B=\left[\begin{array}{lll}-1& 2& 1\end{array}\right]$

If $A=\left[\begin{array}{ll}-2& 3\\ 1& 2\end{array}\right]$ and $B=\left[\begin{array}{ll}-1& 0\\ 1& 2\end{array}\right]$, then find $(A+2B{)}^{\text{'}}$

If $A^{\text{'}}=\left[\begin{array}{ll}3& 4\\ -1& 2\\ 0& 1\end{array}\right]$ and $B=\left[\begin{array}{ccc}-1& 2& 1\\ 1& 2& 3\end{array}\right]$, then verify that $(A-B{)}^{\text{'}}=A^{\text{'}}-B^{\text{'}}$

If $A^{\text{'}}=\left[\begin{array}{ll}3& 4\\ -1& 2\\ 0& 1\end{array}\right]$ and $B=\left[\begin{array}{ccc}-1& 2& 1\\ 1& 2& 3\end{array}\right]$, then verify that $(A+B{)}^{\text{'}}=A^{\text{'}}+B^{\text{'}}$

If $A=\left[\begin{array}{lll}-1& 2& 3\\ 5& 7& 9\\ -2& 1& 1\end{array}\right]$ and $B=\left[\begin{array}{ccc}-4& 1& -5\\ 1& 2& 0\\ 1& 3& 1\end{array}\right]$, then verify that  $(A-B{)}^{\text{'}}=A^{\text{'}}-B^{\text{'}}$

Find the transpose of the following matrix:
 $\left[\begin{array}{l}5\\ \frac{1}{2}\\ -1\end{array}\right]$