Find the values of $x, y, z$ if the matrix $A=\left[\begin{array}{ccc}0 & 2 y & z \\ x & y & -z \\ x & -y & z\end{array}\right]$ satisfy the equation $A^{\prime} A=I$.

If $A = \left[ {\begin{array}{*{20}{c}}{\cos \theta }&{ – \sin \theta }\\{\sin \theta }&{\cos \theta }\end{array}} \right]$, then which of the following statements is not correct

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

The total number of $3 \times 3$ matrices $A$ having enteries from the set $(0,1,2,3)$ such that the sum of all the diagonal entries of $AA ^{ T }$ is $9$, is equal to……..

If $A = \left( {\begin{array}{*{20}{c}}1&{ – 2}&1\\2&1&3\end{array}} \right)$ and $B = \left( {\begin{array}{*{20}{c}}2&1\\3&2\\1&1\end{array}} \right)$, then ${(AB)^T}$ is equal to