If $A$ is a square matrix, then which of the following is true?

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 = $ . . . . . . .

The trace of the matrix $A = \begin{bmatrix} 0 & 7 & 9 \\ 11 & 8 & 9 \end{bmatrix}$ is defined only for square matrices. If we consider the matrix $A = \begin{bmatrix} 1 & -5 & 7 \\ 0 & 7 & 9 \\ 11 & 8 & 9 \end{bmatrix}$,what is its trace?

The matrix $A = \begin{bmatrix} 1/\sqrt{2} & 1/\sqrt{2} \\ -1/\sqrt{2} & -1/\sqrt{2} \end{bmatrix}$ is

If a square matrix $A$ is such that $\left(A^T-\frac{1}{2} I\right)\left(A-\frac{1}{2} I\right) = \left(A^T+\frac{1}{2} I\right)\left(A+\frac{1}{2} I\right) = I$,where $I$ is a unit matrix,then $A$ is

If $A$ is a square matrix,then which of the following matrices is not symmetric?