Suppose the vectors x₁, x₂ and x₃ are the solutions of the system of linear equations, Ax = b when the vector b on the right side is equal to b₁, b₂ and b₃ respectively. if${x_1} = \left[ {\matrix{ 1 \cr 1 \cr 1 \cr } } \right]$, ${x_2} = \left[ {\matrix{ 0 \cr 2 \cr 1 \cr } } \right]$, ${x_3} = \left[ {\matrix{ 0 \cr 0 \cr 1 \cr } } \right]$${b_1} = \left[ {\matrix{ 1 \cr 0 \cr 0 \cr } } \right]$, ${b_2} = \left[ {\matrix{ 0 \cr 2 \cr 0 \cr } } \right]$ and ${b_3} = \left[ {\matrix{ 0 \cr 0 \cr 2 \cr } } \right]$, then the determinant of A is equal to :