If $A$ is a matrix of order $3 \times 3$,then $(A^2)^{-1}$ is equal to

If $A = f(x) = \begin{bmatrix} \cos x & \sin x & 0 \\ -\sin x & \cos x & 0 \\ 0 & 0 & 1 \end{bmatrix}$,then $A^{-1}$ is equal to:

If $K \in R_0$,then $\det(adj(KI_n))$ is equal to:

If a matrix $A$ satisfies the equation $A^3-6A^2+11A-6I=0$,then $A^{-1}$ can be expressed in terms of $A$ as:

If $A = \begin{bmatrix} 1 & -1 & 1 \\ 0 & 2 & -3 \\ 2 & 1 & 0 \end{bmatrix}$,$B = \text{adj}(A)$,and $C = 5A$,then find the value of $\frac{|\text{adj}(B)|}{|C|}$.

Let $A = \begin{bmatrix} 1 & 1 & 2 \\ -2 & 0 & 1 \\ 1 & 3 & 5 \end{bmatrix}$. Then the sum of all elements of the matrix $\text{adj}(\text{adj}(2(\text{adj} A)^{-1}))$ is equal to: