If $A$ is a square matrix,then $A + A^T$ is:

$A, B, C, D$ are square matrices such that $A+B$ is symmetric, $A-B$ is skew-symmetric and $D$ is the transpose of $C$. If $A=\left[\begin{array}{ccc}-1 & 2 & 3 \\ 4 & 3 & -2 \\ 3 & -4 & 5\end{array}\right]$ and $C=\left[\begin{array}{ccc}0 & 1 & -2 \\ 2 & -1 & 0 \\ 0 & 2 & 1\end{array}\right]$, then the matrix $B+D=$

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

If $A = \begin{bmatrix} \cos \theta & \sin \theta \\ -\sin \theta & \cos \theta \end{bmatrix}$,then $A \cdot A^{\prime}$ is

If $A$ is a symmetric matrix,then the matrix $M'AM$ is

For a given matrix $A = \begin{bmatrix} \cos \theta & -\sin \theta \\ \sin \theta & \cos \theta \end{bmatrix}$,which of the following statements holds true?