If for the matrix $A$,${A^3} = I$,then ${A^{-1}} = $

If $A$ and $B$ are non-singular square matrices of the same order,then $adj(AB)$ is equal to:

Let $A = (a_{ij})_{1 \leq i, j \leq 3}$ be a $3 \times 3$ invertible matrix where each $a_{ij}$ is a real number. Denote the inverse of the matrix $A$ by $A^{-1}$. If $\sum_{j=1}^3 a_{ij} = 1$ for $1 \leq i \leq 3$,then:

If $A = \begin{bmatrix} 1 & -2 & 2 \\ 2 & -6 & 5 \\ 5 & 0 & 4 \end{bmatrix}$,then $\operatorname{Adj} A = $

If $A^{-1}=\left[\begin{array}{ccc}3 & -1 & 1 \\ -15 & 6 & -5 \\ 5 & -2 & 2\end{array}\right]$ and $B=\left[\begin{array}{ccc}1 & 2 & -2 \\ -1 & 3 & 0 \\ 0 & -2 & 1\end{array}\right],$ find $(AB)^{-1}$.

If $A = \begin{bmatrix} 1 & 5 \\ \lambda & 10 \end{bmatrix}$,$A^{-1} = \alpha A + \beta I$ and $\alpha + \beta = -2$,then $4\alpha^2 + \beta^2 + \lambda^2$ is equal to: