If $A = \begin{bmatrix} a & 0 & 0 \\ 0 & a & 0 \\ 0 & 0 & a \end{bmatrix}$,then $|A| |adj A|$ is equal to

If the inverse matrix of $A = \begin{bmatrix} 2 & 3 \\ 1 & -4 \end{bmatrix}$ is $A^{-1} = \begin{bmatrix} a & 3/11 \\ 1/11 & b \end{bmatrix}$, then $a+b=$ . . . . . . .

Let $A$ be a $2 \times 2$ matrix.
$Statement-1: adj(adj A) = A$
$Statement-2: |adj A| = |A|$

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 $K \in R_0$,then $\det(adj(KI_n))$ is equal to:

Find $P^{-1},$ if it exists,given $P=\left[\begin{array}{cc}10 & -2 \\ -5 & 1\end{array}\right].$