Use the Appropriate Property of Determinants from This Section to Justify

question 156

Multiple Choice

Use the appropriate property of determinants from this section to justify the true statement. $\left| \begin{array} { c c c } 6 & 9 & 11 \\8 & - 10 & 3 \\6 & 5 & - 1\end{array} \right| = - \left| \begin{array} { c c c } 6 & 11 & 9 \\8 & 3 & - 10 \\6 & - 1 & 5\end{array} \right|$ Do not evaluate the determinants.

• A) Property number 1: If any row (or column) of a square matrix A contains only zeros, then | A | = 0.
• B) Property number 3: If square matrix B is obtained from square matrix A by multiplying each element of any row (or column) of A by some real number k , then | B | = k | A |.
• C) Property number 4: If square matrix B is obtained from square matrix A by adding k times a row (or column) of A to another row (or column) of A , then | B | = | A |.
• D) Property number 2: If square matrix B is obtained from square matrix A by interchanging two rows (or two columns), then | B | = \(-\) | A |.
• E) Property number 5: If two rows (or columns) of a square matrix A are identical, then | A | = 0.