If $A$ is a $2 \times 2$ order non-singular matrix,then the determinant of $A^{-1}$ is . . . . . . .

Find the inverse of the matrix (if it exists): $\left[\begin{array}{ccc}1 & 0 & 0 \\ 0 & \cos a & \sin a \\ 0 & \sin a & -\cos a\end{array}\right]$

Let $A$ be any $3 \times 3$ invertible matrix. Then which one of the following is not always true?

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

If $A = \begin{bmatrix} -2 & 2 \\ -3 & 2 \end{bmatrix}$ and $B = \begin{bmatrix} 0 & -1 \\ 1 & 0 \end{bmatrix}$,then $(B^{-1} A^{-1})^{-1}$ is equal to

If possible,using elementary row transformations,find the inverse of the following matrix: $\left[\begin{array}{ccc}2 & 3 & -3 \\ -1 & -2 & 2 \\ 1 & 1 & 1\end{array}\right]$