The inverse of a symmetric matrix is

If $A = \begin{bmatrix} a & 1 & 2 \\ 1 & 2 & b \\ c & 1 & 3 \end{bmatrix}$ and $\operatorname{Adj} A = \begin{bmatrix} 7 & -1 & -5 \\ -3 & 9 & 5 \\ 1 & -3 & 5 \end{bmatrix}$,then $a^2 + b^2 + c^2 = $

If $B=\left[\begin{array}{ll}1 & 3 \\ 1 & \alpha\end{array}\right]$ is the adjoint of a matrix $A$ and $|A|=2$,then the value of $\alpha$ is

If $A$ and $B$ are two matrices given by $A = \begin{bmatrix} 1 & 2 & 3 \\ 2 & 3 & 4 \\ 5 & 6 & 8 \end{bmatrix}$ and $B = \begin{bmatrix} 3 & 2 & 5 \\ 2 & 3 & 8 \\ 7 & 2 & 9 \end{bmatrix}$,then the value of $|\operatorname{Adj}(AB)|$ is

If $A$ is a $3 \times 3$ matrix such that $|5 \cdot \text{adj } A| = 5$,then $|A|$ is equal to

If $A$ is a $n \times n$ matrix,then $adj(adj \,A) = $