Final answer:
Swapping two rows of a matrix changes the sign of its determinant. Therefore, if det(A) = 2 for a 5x5 matrix A, after swapping the second and fourth rows to get matrix C, det(C) will be -2.
Step-by-step explanation:
If the determinant of a 5x5 matrix A is det(A) = 2, and the matrix C is obtained from A by swapping the second and fourth rows, then the determinant of matrix C, det(C), is affected by this row swap operation. In linear algebra, swapping two rows of a matrix results in the determinant of the new matrix having the opposite sign of the original determinant. Hence, if det(A) = 2, after swapping two rows to get matrix C, the determinant will be det(C) = -2.