Final answer:
The determinant of the matrix changes to -2 after switching two columns, based on the property that swapping rows or columns of a matrix multiplies its determinant by -1.
Step-by-step explanation:
The student is asking about the determinant of a matrix and how switching columns affects the determinant value. The original determinant of the matrix |[ a b c; d e f; g h i ]| is given as 2. When we switch columns (here the second and third columns), the determinant of the new matrix |[ a c b; d f e; g i h ]| becomes the opposite of the original determinant. Therefore, the determinant of the new matrix is -2. This is based on the property that interchanging any two rows or columns of a square matrix multiplies its determinant by -1.