The trace of the matrix $$A=\left[\begin{array}{ccc}1 & -5 & 7 \\ 0 & 7 & 9 \\ 11 & 8 & 9\end{array}\right]$$ is

If $$A, B$$ and $$C$$ are the angles of a triangle, then the system of equations $$-x+y \cos C+z \cos B=0, x \cos C-y+z \cos A=0$$ and $$x \cos B+y \cos A-z=0$$

If $$\left[\begin{array}{cc}1 & -\tan \theta \\ \tan \theta & 1\end{array}\right]\left[\begin{array}{cc}1 & \tan \theta \\ -\tan \theta & 1\end{array}\right]^{-1} =\left[\begin{array}{cc}a & -b \\ b & a\end{array}\right]$$, then

What is the value of $$\left|\begin{array}{ccc}a & b & c \\ a-b & b-c & c-a \\ b+c & c+a & a+b\end{array}\right|$$ ?