Use the Appropriate Property of Determinants from This Section to Justify

Multiple Choice

Use the appropriate property of determinants from this section to justify the true statement. $$\left| \begin{array} { c c c } 12 & 3 & 3 \\4 & - 1 & 9 \\20 & - 5 & 15\end{array} \right| = 12 \left| \begin{array} { c c c } 3 & 3 & 1 \\1 & - 1 & 3 \\5 & - 5 & 5\end{array} \right| = 60 \left| \begin{array} { c c c } 3 & 3 & 1 \\1 & - 1 & 3 \\1 & - 1 & 1\end{array} \right|$$ Do not evaluate the determinants.

A) 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 |.
B) Property number 2: If square matrix B is obtained from square matrix A by interchanging two rows (or two columns) , then | B | = $-$ | 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 1: If any row (or column) of a square matrix A contains only zeros, then | A | = 0.
E) Property number 5: If two rows (or columns) of a square matrix A are identical, then | A | = 0.