Browse Questions

# If $A$ is a $3\times 3$ matrix, and $|A|\neq0$ and $|3A|=k.|A|,$ then write the value of $k$

Toolbox:
• If $|A|=x$, then $|p.A|=p^n.|A|$ where $n$ is order of the matrix $A$.
Given: $|3A|=k.|A|$
We know that $|3A|=3^n.|A|$ where $n$ is order of $A$.
Given that order of $A$ is $3$.
$\Rightarrow\:|3A|=3^3.|A|=k.|A|$
$\Rightarrow\:k=27$