If $A = \begin{bmatrix} 3 & 2 \\ 1 & 4 \end{bmatrix}$,then $A(\text{adj } A) = $

If matrix $A = \begin{bmatrix} 1 & 2 \\ 3 & 5 \end{bmatrix}$ and $A^{-1} = \alpha I + \beta A$ where $I$ is a unit matrix of order $2$ and $\alpha, \beta$ are constants,then the value of $\alpha + \beta + \alpha \beta$ is

If $k$ is a scalar and $I$ is a unit matrix of order $3$,then $adj(kI) = $

If $A$ and $B$ are square matrices of the same order and $|B| \neq 0$,then $(B^{-1}AB)^5$ is equal to

If $\begin{bmatrix} 2 & 1 \\ 3 & 2 \end{bmatrix} A = \begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}$,then the matrix $A$ is

If $A = \begin{bmatrix} 1 & 0 & 0 \\ 0 & 1 & 1 \\ 0 & -2 & 4 \end{bmatrix}$ and $I = \begin{bmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{bmatrix}$,and $A^{-1} = \frac{1}{6}[A^2 + cA + dI]$ where $c, d \in R$,then the pair of values $(c, d)$ is: