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.(a) Adding a multiple of one column of a square matrix to another column changes only the sign of the determinant. (b) Two matrices are column-equivalent when one matrix can be obtained by performing elementary column operations on the other. (c) If one row of a square matrix is a multiple of another row, then the determinant is 0.

Question

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.
(a) Adding a multiple of one column of a square matrix to another column changes only the sign of the determinant.
(b) Two matrices are column-equivalent when one matrix can be obtained by performing elementary column operations on the other.
(c) If one row of a square matrix is a multiple of another row, then the determinant is 0.

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