Determine whether each statement is true or false. If a statement is true, give a reason or cite an appropriate statement from the text. If a statement is false, provide an example that shows the statement is not true in all cases or cite an appropriate statement from the text. 1. Adding a multiple of one column of a square matrix to another column changes only the sign of the determinant.

a. False, adding a multiple of one column to another does not change the value of the determinant.
b. False, adding a multiple of one column to another changes the sign of the determinant.
c. True, adding a multiple of one column to another changes only the sign of the determinant.
d. False, adding a multiple of one column to another changes the value of the determinant by the multiple of the minor.

2. Two matrices are column-equivalent when one matrix can be obtained by performing elementary column operations on the other.

a. False, row-equivalent matrices are matrices that can be obtained from each other by performing elementary column operations on the other.
b. True, column-equivalent matrices are matrices that can be obtained from each other by performing elementary row operations on the other.
c. False, row-equivalent matrices are matrices that can be obtained from each other by performing elementary row operations on the other.
d. True, column-equivalent matrices are matrices that can be obtained from each other by performing elementary column operations on the other.