For any square matrix $A$,$AA^T$ is a

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

Let $X$ and $Y$ be two arbitrary,$3 \times 3$,non-zero,skew-symmetric matrices and $Z$ be an arbitrary $3 \times 3$,non-zero,symmetric matrix. Then which of the following matrices is (are) skew-symmetric?
$(A) Y^3 Z^4 - Z^4 Y^3$
$(B) X^{44} + Y^{44}$
$(C) X^4 Z^3 - Z^3 X^4$
$(D) X^{23} + Y^{23}$

For a square matrix $A$,if $A = B + \frac{C}{2}$,where $B$ is a skew-symmetric matrix and $C$ is a symmetric matrix,then $C = $ . . . . . . .

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

If the matrix $A$ is both symmetric and skew-symmetric,then