If $A$ is a non-singular matrix,then $A(\text{adj } A) =$

If $A$ is a $3 \times 3$ non-singular matrix such that $AA' = A'A$ and $B = A^{-1}A'$,then $BB'$ equals:

If $A = \begin{bmatrix} \sin \alpha & -\cos \alpha \\ \cos \alpha & \sin \alpha \end{bmatrix}$ and $A + A^{-1} = I$,then $\alpha =$

If $A, B$ and $(\operatorname{adj}(A^{-1})+\operatorname{adj}(B^{-1}))$ are non-singular matrices of the same order,then the inverse of $A(\operatorname{adj}(A^{-1})+\operatorname{adj}(B^{-1}))^{-1}B$ is equal to

If $A = \begin{bmatrix} 2 & 3 \\ 4 & 6 \end{bmatrix}$,then ${A^{-1}} = $

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