A matrix of order 3 × 3 has determinant 2.


A matrix of order $3 \times 3$ has determinant 2 . What is the value of $|A(3 D)|$, where $/$ is the identity matrix of order $3 \times 3$.


Let $A$ be the given matrix. Then,

$|A|=2 \quad[$ Order $=n=3]$

$|I|=1 \quad[I$ is an identity matrix $]$


$|A 3(\mathrm{I})|=|3 A|=3^{3}|A|$            $[A$ being of order 3$]$

$=27 \times 2=54$

$\Rightarrow|A 3(\mathrm{I})|=54$

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