For the matrix $A=\left[\begin{array}{ll}1 & 5 \\ 6 & 7\end{array}\right],$ verify that $(A-A^{\prime})$ is a skew symmetric matrix

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

Let $A$ be a symmetric matrix such that $|A|=2$ and $\left[\begin{array}{ll}2 & 1 \\ 3 & \frac{3}{2}\end{array}\right] A =\left[\begin{array}{ll}1 & 2 \\ \alpha & \beta\end{array}\right]$. If the sum of the diagonal elements of $A$ is s, then $\frac{\beta s}{\alpha^2}$ is equal to $……….$.

Let $A$ and $B$ be any two $3\times3$ matrices. If $A$ is symmetric and $B$ is skewsymmetric, then the matrix $AB – BA$ is

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