If $A = \begin{bmatrix} 3 & -3 & 4 \\ 2 & -3 & 4 \\ 0 & -1 & 1 \end{bmatrix}$,then $A A^T$ is a

For the matrix $A = \begin{bmatrix} 1 & 5 \\ 6 & 7 \end{bmatrix}$,verify that $(A + A^{\prime})$ is a symmetric matrix.

If $A$ is a symmetric matrix and $B$ is a skew-symmetric matrix such that $A + B = \begin{bmatrix} 2 & 3 \\ 5 & -1 \end{bmatrix}$,then $AB$ is equal to

If $A = \begin{bmatrix} 5 & 2x+3 \\ x-2 & x+1 \end{bmatrix}$ is a symmetric matrix,then $x$ is equal to:

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

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?