Question

Let $A$ be a square matrix of order $n$ such that $det\left(A\right)=10$ and $\frac{det\left(2A\right)}{2}=40.$ Then the order of $A$ is

[1 mark]

• A. $2$
• B. $3$
• C. $4$
• D. $6$

Answer 1

The correct option is B $3$

We know that,
$det\left(KA\right)=K^n\cdot det\left(A\right)$
$\Rightarrow det\left(2A\right)=2^n\cdot det\left(A\right)$
$\Rightarrow \frac{det\left(2A\right)}{2}=2^{n-1}\cdot det\left(A\right)$
$\Rightarrow 40=2^{n-1}\times 10$
$\Rightarrow 2^{n-1}=4$
$\Rightarrow n=3$ (order of matrix $A$)