Discussion
Consider the following statements about determinants.
1. Interchanging two rows changes the sign 2. Adding a multiple of one row to another leaves the value unchanged 3. For a matrix of order n, the determinant of kA is k times that of A
Answer: C
Correct answer: 1 and 2 only are correct
Statements 1 and 2 are standard properties: a row interchange reverses the sign, and adding a multiple of one row to another leaves the value unchanged, which is what makes elimination safe. Statement 3 is wrong - scaling the whole matrix scales every row, so \( |kA| = k^{n}|A| \), not \( k|A| \).
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