If $A, B$ are two square matrices, such that $A B=A, B A=B$, then $(A+B)^7$ equals

If $A=\left[\begin{array}{ll}1 & 1 \\ 0 & 1\end{array}\right]$ and $B=\left[\begin{array}{cc}\frac{\sqrt{3}}{2} & \frac{1}{2} \\ -\frac{1}{2} & \frac{\sqrt{3}}{2}\end{array}\right]$, then $\left(B B^T A\right)^5$ is equal to

If matrix $$A=\left[\begin{array}{ccc}0 & 2 b & -2 \\ 3 & 1 & 3 \\ 3 a & 3 & -1\end{array}\right]$$ is given to be symmetric, then the value of $$a b$$ is

The determinant of the matrix $$\left[\begin{array}{ccc}1 & 4 & 8 \\ 1 & 9 & 27 \\ 1 & 16 & 64\end{array}\right]$$ is