Question:
Let $\mathrm{A}$ be a $3 \times 3$ matrix with $\operatorname{det}(\mathrm{A})=4$. Let $\mathrm{R}_{\mathrm{i}}$ denote the $\mathrm{i}^{\text {th }}$ row of $\mathrm{A}$. If a matrix $\mathrm{B}$ is obtained by performing the operation $\mathrm{R}_{2} \rightarrow 2 \mathrm{R}_{2}+5 \mathrm{R}_{3}$ on $2 \mathrm{~A}$, then $\operatorname{det}(\mathrm{B})$ is equal to :
Correct Option: , 4
Solution:
$|\mathrm{A}|=4$
$\Rightarrow|2 \mathrm{~A}|=2^{3} \times 4=32$
$\because \mathrm{B}$ is obtained by $\mathrm{R}_{2} \rightarrow 2 \mathrm{R}_{2}+5 \mathrm{R}_{3}$
$\Rightarrow|B|=2 \times 32=64$
option (4)
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