Final answer:
An elementary row operation on a matrix can change the determinant, depending on the type of operation. Scaling a row does not affect the determinant, but swapping rows changes the sign and adding a multiple of one row does not change the determinant.
Step-by-step explanation:
An elementary row operation is a specific manipulation that can be performed on the rows of a matrix. There are three types of elementary row operations: 1) Scaling a row by a non-zero constant, 2) Swapping two rows, and 3) Adding a multiple of one row to another row.
When you perform an elementary row operation on a matrix, the determinant of the matrix may change. The scalar multiplication operation does not affect the determinant, but the row swapping and row addition operations can change the determinant.
For example, if you swap two rows of a matrix, the determinant will change sign. If you add a multiple of one row to another row, the determinant remains unchanged.