If $A$ is a non-singular matrix such that $A \cdot A^T = A^T \cdot A$ and $B = A^{-1} \cdot A^T$,then

If $A$ and $B$ are non-singular square matrices of the same order,then $adj(AB)$ is equal to:

If $\operatorname{adj} B = A$ and $|P| = |Q| = 1$, then $\operatorname{adj}(Q^{-1} B P^{-1}) = $

Let $A$ be a non-singular matrix of order $n$ and $|A|=k$, then $(\operatorname{adj} A)^{-1}$ is

Let $A = \left[ {\begin{array}{*{20}{c}}1&0&0\\2&1&0\\3&2&1\end{array}} \right]$. If $u_1$ and $u_2$ are column matrices such that $A{u_1} = \left[ {\begin{array}{*{20}{c}}1\\0\\0\end{array}} \right]$ and $A{u_2} = \left[ {\begin{array}{*{20}{c}}0\\1\\0\end{array}} \right]$,then $u_1 + u_2$ is equal to:

Let $A$ be a $3 \times 3$ matrix such that $A+A^{T}=O$. If $A\begin{bmatrix}1\\ -1\\ 0\end{bmatrix}=\begin{bmatrix}3\\ 3\\ 2\end{bmatrix}$, $A^{2}\begin{bmatrix}1\\ -1\\ 0\end{bmatrix}=\begin{bmatrix}-3\\ 19\\ -24\end{bmatrix}$ and $\det(\text{adj}(2\text{adj}(A+I))) = (2)^\alpha \cdot(3)^\beta \cdot(11)^\gamma$, then $\alpha+\beta+\gamma$ is equal to . . . . . . .