Question:
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 $3 \times 3$.
Solution:
Let $A$ be the given matrix. Then,
$|A|=2 \quad[$ Order $=n=3]$
$|I|=1 \quad[I$ is an identity matrix $]$
$3(\mathrm{I})=3$
$|A 3(\mathrm{I})|=|3 A|=3^{3}|A|$ $[A$ being of order 3$]$
$=27 \times 2=54$
$\Rightarrow|A 3(\mathrm{I})|=54$
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