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

If $A = \left[ {\begin{array}{*{20}{c}}
1&1\\
0&1
\end{array}} \right]$ and $B = \left[ {\begin{array}{*{20}{c}}
{\frac{{\sqrt 3 }}{2}}&{\frac{1}{2}}\\
{\frac{{ – 1}}{2}}&{\frac{{\sqrt 3 }}{2}}
\end{array}} \right]$ , then $(BB^TA)^5$ is equal to

The number of symmetric matrices of order $3$, with all the entries from the set $\{0,1,2,3,4,5,6,7,8,9\}$, is :

If $ A$  is a symmetric matrix and $n \in N$, then ${A^n}$ is

Let $A$ be a symmetric matrix of order $2$ with integer entries. If the sum of the diagonal elements of $A ^{2}$ is $1,$ then the possible number of such matrices is