Adjoint Properties

Q.

If $A=\left[\begin{array}{ccc}1& 2& 3\\ 0& 4& 5\\ 0& 0& 1\end{array}\right]$, then $det\left(A^{-1}\right)$ is ________. (correct to two decimal places)

1. 0.25

Q. For a given matrix A of 3 x 3 order, find |Adj(A)|
Where, $A=\left[\begin{array}{ccc}1& 2& 1\\ 0& 5& 1\\ 1& 4& 3\end{array}\right]$

1. 8
2. 32
3. 64
4. 512

Q. A $3\times 3$ matrix is defined as
The values of $x$ required for which $A^{-1}$ can't be determined will be
$A=\left[\begin{array}{ccc}3-x& 2& 2\\ 2& 4-x& 1\\ -2& -4& -1-x\end{array}\right]$

1. 0, 3, 3
2. 0, 1, 3
3. 0, -1, 4
4. 1, -1, 3