Question

A matrix $A$ of order $3\times 3$ has determinant $6$. What is the value of $|3A|$?

Answer 1

We know that,

For a matrix of order $n\times n$, $\left|kA\right|=k^n\left|A\right|$

In the given matrix $A$,

$n=3$ and $\left|A\right|=6$

To find,

$\left|3A\right|$

$⟹k=3$

$\therefore \left|kA\right|=k^n\left|A\right|$

$\left|3A\right|=3^3\left(6\right)=162$