Let A be a square matrix of order $3 \times 3$. If $|A|=-4$, then the value of $\left|\frac{A^{-1}}{-2}\right|$ is:

Matrix $A=\left[\begin{array}{ccc}1 & 1 & 2 \\ 1 & -2 & 2 \\ 1 & 0 & -1\end{array}\right]$,

Given $\boldsymbol{M}_{\mathbf{2 2}}$ and $\boldsymbol{A}_{\mathbf{3 2}}$ are the minor and cofactor of the adjoint matrix of $\boldsymbol{A}$ respectively then the value of the expression $\boldsymbol{M}_{\mathbf{2 2}}+\boldsymbol{A}_{\mathbf{3 2}}-|\boldsymbol{a} \boldsymbol{d} \boldsymbol{j}|$ is:

Let $A=\left[a_{i j}\right]$ be a square matrix of order $3 \times 3$, where the elements are defined as $a_{i j}=\left\{\begin{array}{ll}i-2 j & \text { if } i=j \\ 0 & \text { if } i> j \\ 1 & \text { if } i < j\end{array} \quad\right.$ then the value of $\left|A^t\right|$ is

Given $A=\left[\begin{array}{lll}x & 1 & -2\end{array}\right]$ and $B=\left[\begin{array}{lll}1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9\end{array}\right]$ If $\boldsymbol{A} \boldsymbol{B} \boldsymbol{A}^{\boldsymbol{t}}=[-\mathbf{2 0}]$ then the value of $\boldsymbol{x}$ is: