If $A$ is a $3 \times 3$ order skew-symmetric matrix,then $|A|$ is equal to:

If $A = \begin{bmatrix} \cos 2\theta & -\sin 2\theta \\ \sin 2\theta & \cos 2\theta \end{bmatrix}$ and $A + A^{T} = I$, where $I$ is the $2 \times 2$ identity matrix and $A^{T}$ is the transpose of $A$, then the value of $\theta$ is:

If $A = \begin{bmatrix} 1 \\ 2 \\ 3 \end{bmatrix}$,then $AA' = $

If $A$ and $B$ are symmetric matrices,then $ABA$ is

Find the transpose of the following matrix: $\left[\begin{array}{cc}1 & -1 \\ 2 & 3\end{array}\right]$

If $A$ and $B$ are skew-symmetric matrices of the same order,then $(AB)^{\prime} =$ . . . . . . .