If $A=\begin{bmatrix} \cos \alpha & -\sin \alpha & 0 \\ \sin \alpha & \cos \alpha & 0 \\ 0 & 0 & 1 \end{bmatrix}$,then $(\operatorname{Adj} A)^{-1}=$

Let $I$ be the identity matrix of order $3 \times 3$ and for the matrix $A = \begin{bmatrix} \lambda & 2 & 3 \\ 4 & 5 & 6 \\ 7 & -1 & 2 \end{bmatrix}$,$|A| = -1$. Let $B$ be the inverse of the matrix $\operatorname{adj}(A \operatorname{adj}(A^2))$. Then $|\lambda B + I|$ is equal to . . . . . . .

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:

The characteristic equation of a matrix $A$ is $\lambda^{3}-5 \lambda^{2}-3 \lambda+2=0$. Then $|\text{adj}(A)|$ is equal to:

If $A=\left[\begin{array}{ll}2 & 3 \\ 1 & 2\end{array}\right]$ and $B=\left[\begin{array}{cc}2 & -3 \\ -1 & 2\end{array}\right]$,then $\left(B^{-1} A^{-1}\right)^{-1}=$

The inverse of $\begin{bmatrix} 2 & -3 \\ -4 & 2 \end{bmatrix}$ is