Matrices may be long.

If

$A = \begin{bmatrix} 1 & 0 & 0 \\ 2 & 1 & 0 \\ 3 & 2 & 1 \\ \end{bmatrix}$

and $U_1 , U_2$ and $U_3$ are column matrices satisfying

$AU_1 = \begin{bmatrix} 1 \\ 0 \\ 0 \\ \end{bmatrix}$

$AU_2 = \begin{bmatrix} 2 \\ 3 \\ 0 \\ \end{bmatrix}$

$AU_3 = \begin{bmatrix} 2 \\ 3 \\ 1 \\ \end{bmatrix}$

and $U$ is a $3 \times 3$ matrix whose columns $C_1 , C_2 , C_3$ are $U_1 , U_2 , U_3$ respectively, then the value of $|U|$ is

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