Let $A = \begin{bmatrix} 1 & 2 \\ -2 & 1 \end{bmatrix}$ and $B^{-1} = \begin{bmatrix} 1 & 1 \\ 0 & 2 \end{bmatrix}$. If $(A B^{-1})^{-1} = \begin{bmatrix} a & b \\ c & d \end{bmatrix}$,then $2b + 5c + 10d =$

If $A = \begin{bmatrix} 4 & 2 \\ 3 & 4 \end{bmatrix}$,then $|adj\,A|$ is equal to

Find the inverse of the matrix (if it exists): $\left[\begin{array}{ccc}2 & 1 & 3 \\ 4 & -1 & 0 \\ -7 & 2 & 1\end{array}\right]$

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 . . . . . . .

If ${A^2} - A + I = 0$,then ${A^{-1}} = $

If $A = \begin{bmatrix} 1 & 1 & 1 \\ 1 & a & 3 \\ 3 & 2 & 2 \end{bmatrix}$ and $B = \begin{bmatrix} -2 & 0 & b \\ 7 & -1 & -2 \\ c & 1 & 1 \end{bmatrix}$ and if matrix $B$ is the inverse of matrix $A$,then the value of $4a + 2b - c$ is: