Question

Let $A$ be a $3 \times 3$ matrix with det $( A )=4$. Let $R _{ i }$ denote the $i ^{\text {th }}$ row of $A$. If a matrix $B$ is obtained by performing the operation $R _{2} \rightarrow 2 R _{2}+5 R _{3}$ on $2 A ,$ then det $( B )$ is equal to :

• A. 16
• B. 80
• C. 128
• D. 64

Answer 1

Answer: (D)

$\mid A| =4$
$\Rightarrow \mid 2 A| =2^{3} \times 4=32$
$\because B$ is obtained by $R _{2} \rightarrow 2 R _{2}+5 R _{3}$
$\Rightarrow | B |=2 \times 32=64$