If $A, B, C$ are three square matrices such that $AB = AC$ implies $B = C$,then the matrix $A$ is always a/an

If $A = \begin{bmatrix} \cos \alpha & \sin \alpha \\ -\sin \alpha & \cos \alpha \end{bmatrix}$ and $A \text{ adj } A = \begin{bmatrix} k & 0 \\ 0 & k \end{bmatrix}$,then $k$ 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:

The inverse of the matrix $\left[\begin{array}{ccc}7 & -3 & -3 \\ -1 & 1 & 0 \\ -1 & 0 & 1\end{array}\right]$ is

If $M$ is any square matrix of order $3$ over $\mathbb{R}$ and if $M^{\prime}$ is the transpose of $M$, then $\text{adj}(M^{\prime}) - (\text{adj } M)^{\prime}$ is equal to

Find the adjoint of the matrix $A = \left[\begin{array}{ccc}1 & -1 & 2 \\ 2 & 3 & 5 \\ -2 & 0 & 1\end{array}\right]$.