If a matrix $A$ is such that $3A^3 + 2A^2 + 5A + I = 0$,then its inverse is

Let $A$ be a $3 \times 3$ matrix such that $\operatorname{adj} A = \begin{bmatrix} 2 & -1 & 1 \\ -1 & 0 & 2 \\ 1 & -2 & -1 \end{bmatrix}$ and $B = \operatorname{adj}(\operatorname{adj} A)$. If $|A| = \lambda$ and $|(B^{-1})^T| = \mu$,then the ordered pair $(|\lambda|, \mu)$ is equal to

If $A = \begin{bmatrix} 3 & 2 \\ 0 & 1 \end{bmatrix}$,then $(A^{-1})^3 = $

Let $A = \begin{bmatrix} 1 & 2 \\ 0 & 1 \end{bmatrix}$ and $B = I + \operatorname{adj}(A) + (\operatorname{adj} A)^2 + \dots + (\operatorname{adj} A)^{10}$. Then,the sum of all the elements of the matrix $B$ is:

If $A = \begin{bmatrix} 1 & 2 & 1 \\ 2 & 1 & 0 \end{bmatrix}$ and $B = \begin{bmatrix} 1 & 2 \\ 2 & 1 \\ 0 & 1 \end{bmatrix}$,then $(AB)^{-1}$ is

If $P = \begin{bmatrix} 1 & \alpha & 3 \\ 1 & 3 & 3 \\ 2 & 4 & 4 \end{bmatrix}$ is the adjoint of a $3 \times 3$ matrix $A$ and $|A| = 4$,then the value of $\alpha$ is: