Matrices And Determinants

$$A=\left[\begin{array}{lll}1 & 0 & 0 \\ 2 & 1 & 0 \\ 3 & 2 & 1\end{array}\right]$$, if \(U_{1}, U_{2}\) and \(U_{3}\) are columns matrices satisfying. $$\mathrm{AU}_{1}=\left[\begin{array}{l}1 \\ 0 \\ 0\end{array}\right], \quad \mathrm{AU}_{2}=\left[\begin{array}{l}2 \\ 3 \\ 0\end{array}\right], \quad \mathrm{AU}_{3}=\left[\begin{array}{l}2 \\ 3 \\ 1\end{array}\right]$$ and \(\mathrm{U}\) is \(3 \times 3\) matrix whose columns are \(\mathrm{U}_{1}, \mathrm{U}_{2}, \mathrm{U}_{3}\) then answer the following questions