13. Let $n$ be an integer, $n \geq 4$. $A$ is an $n \times n$ matrix with real entries. The matrix $B$ is obtained by the following sequence of operations on $A$. First, multiply each entry of $A$ by 2 . Then add 3 times the second column to the third column. Finally, swap the first and the fourth columns. If $\operatorname { det } ( A ) = 5$, which of the following statements are true? (a) 10 divides $\operatorname { det } ( B )$ (b) $\operatorname { det } ( B ) = - 5$ (c) 100 divides $\operatorname { det } ( B )$ (d) $\operatorname { det } ( B ) = - 2 ^ { n } \cdot 5$
13. Let $n$ be an integer, $n \geq 4$. $A$ is an $n \times n$ matrix with real entries. The matrix $B$ is obtained by the following sequence of operations on $A$. First, multiply each entry of $A$ by 2 . Then add 3 times the second column to the third column. Finally, swap the first and the fourth columns. If $\operatorname { det } ( A ) = 5$, which of the following statements are true?\\
(a) 10 divides $\operatorname { det } ( B )$\\
(b) $\operatorname { det } ( B ) = - 5$\\
(c) 100 divides $\operatorname { det } ( B )$\\
(d) $\operatorname { det } ( B ) = - 2 ^ { n } \cdot 5$\\