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:

If A and B are two square matrices of the same order such that $\mathrm{AB}=\mathrm{A}$ and $\mathrm{BA}=\mathrm{B}$, then $(\boldsymbol{A}+\boldsymbol{B})^2$ is equal to:

If $x=4$ is a root of $\left|\begin{array}{cc}x & 3 \\ 1 & x-2\end{array}\right|=5$, then the other root is: