Q8Multiple correct5 Marks13 Jul 2025

Let $A$ be a $3\times3$ matrix such that $\det(A)=-3$. For which of the options below is the matrix $B$, obtained from $A$ by performing the operations in the option, such that $\det(B)=12$?

A

$B$ is obtained by swapping the first two rows and then multiplying the third row by $4$.

B

$B$ is obtained by swapping the first and third row and then multiplying the second row by $-4$.

C

$B$ is obtained by multiplying the second row by $-4$.

D

$B$ is obtained by multiplying the first row by $2$ and the third row by $-2$.