If $\left[\begin{array}{ccc}-1 & 2 & b \\ a & 5 & 6 \\ 3 & c & 7\end{array}\right]$ is a symmetric matrix, then $\left|\begin{array}{lll}a & b & c \\ b & c & a \\ c & a & b\end{array}\right|=$

If the matrix $A=\left[\begin{array}{lll}1 & 2 & 2 \\ 2 & 1 & 2 \\ 2 & 2 & 1\end{array}\right]$ satisfies the matrix equation $A^2-4 A-5 I=0$, then $A^{-1}=$

Consider the simultaneous linear equations $A X=B$ and $A Y=Q$. If $A$ is an invertible matrix and $B$ is the unique solution of $A Y=Q$, then the solution of $A X=B$ is

If $f(x)=\left|\begin{array}{ccc}-\sin x & 2 \sin 2 x & 4 \cos ^2 x \\ \cos x & 4 \sin ^2 x & 2 \sin 2 x \\ 0 & -\cos x & \sin x\end{array}\right|$, then $f\left(\frac{5 \pi}{4}\right)+f^{\prime}\left(\frac{5 \pi}{4}\right)=$