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 $A^{\prime} A=I$.

The matrix $A = \frac{1}{3}\left[ {\begin{array}{*{20}{c}}1&2&2\\2&1&{ – 2}\\{ – 2}&2&{ – 1}\end{array}} \right]$is

Let $A=\left[\begin{array}{ll}2 & 3 \\ a & 0\end{array}\right], a \in R$ be written as $P+Q$ where $P$ is a symmetric matrix and $Q$ is skew symmetric matrix. If $\operatorname{det}(Q)=9$, then the modulus of the sum of all possible values of determinant of $P$ is equal to:

If $A',B'$ are transpose matrices of the square matrices $A,B$ respectively , then $(AB)'$is equal to

For two $3\times3$ matrices $A$ and $B$ , let $A+ B\, = 2B'$ and $3A + 2B\, = I_3$, where $B'$ is the transpose of $B$ and $I_3$ is $3\times3$ identity matrix. Then