If $AA^T = I$ and $C$ is skew symmetric matric then $((A^T CA)^{50})^T$ 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

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 $……….$.

The product of a matrix and its transpose is an identity matrix. the value of determinant of this matrix is

If $A$ and $B$ are symmetric matrices, prove that $A B-B A$ is a skew symmetric matrix.