Let $A$ be a square matrix of order $3$ whose all entries are $1$ and let $I_{3}$ be the identity matrix of order $3$. Then,the matrix $A-3I_{3}$ is

Matrix $A = \begin{bmatrix} x & 3 & 2 \\ 1 & y & 4 \\ 2 & 2 & z \end{bmatrix}$. If $xyz = 60$ and $8x + 4y + 3z = 20$,then $A (adj A)$ is equal to:

If $A = \begin{bmatrix} 0 & 1+2i & i-2 \\ -1-2i & 0 & K \\ 2-i & -7 & 0 \end{bmatrix}$ and $A^{-1}$ does not exist,then $K = $ (where $i = \sqrt{-1}$)

Let $A = \begin{bmatrix} 0 & 0 & -1 \\ 0 & -1 & 0 \\ -1 & 0 & 0 \end{bmatrix}$ and $B = \begin{bmatrix} 0 & 1 & 0 \\ 1 & 0 & 0 \\ 0 & 0 & 1 \end{bmatrix}$. Then find the value of $(A^{-1}B)^{-1} + (AB^{-1})^{-1}$.

If $A = \begin{bmatrix} 1 & \tan \frac{\alpha}{2} \\ -\tan \frac{\alpha}{2} & 1 \end{bmatrix}$ and $AB = I$,then $B$ is equal to

Find the inverse of the matrix,if it exists: $\left[\begin{array}{ll}1 & 3 \\ 2 & 7\end{array}\right]$