Question

Let $A$ be a square matrix of order $3\times 3$. Write the value of $|2A|$, where $|A|=4.$

Answer 1

In a square matrix of order $3\times 3$, $\left|kA\right|=k^3\left|A\right|$

$\therefore \left|2A\right|=2^3\left|A\right|$

Since $\left|A\right|=4$ therefore,

$\left|2A\right|=2^3\left|A\right|=2^3\left(4\right)=8\left(4\right)=32$

Hence, $\left|2A\right|=32$.