If $A = \begin{bmatrix} 2 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 3 \end{bmatrix}$,then the sum of all elements of $A^{-1}$ is . . . . . . .

Using elementary transformations,find the inverse of the following matrix,if it exists: $A = \begin{bmatrix} -1 & 2 \\ -3 & 5 \end{bmatrix}$

If $\begin{bmatrix} 2 & 1 \\ 3 & 2 \end{bmatrix} A = \begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}$,then the matrix $A$ is

If $P = \begin{bmatrix} 1 & \alpha & 3 \\ 1 & 3 & 3 \\ 2 & 4 & 4 \end{bmatrix}$ is the adjoint of a $3 \times 3$ matrix $A$ and $|A| = 4$,then the value of $\alpha$ is:

Let $A = \left[ {\begin{array}{*{20}{c}}1&0&0\\2&1&0\\3&2&1\end{array}} \right]$. If $u_1$ and $u_2$ are column matrices such that $A{u_1} = \left[ {\begin{array}{*{20}{c}}1\\0\\0\end{array}} \right]$ and $A{u_2} = \left[ {\begin{array}{*{20}{c}}0\\1\\0\end{array}} \right]$,then $u_1 + u_2$ is equal to:

If $A^{-1}=\frac{-1}{2}\left[\begin{array}{cc}5 & 8 \\ -1 & 2\end{array}\right]$,then $2A+I_2=$,where $I_2$ is a unit matrix of order $2$.