Question:
If $A$ and $B$ are non-singular square matrices of order $n$ such that $A=k B$, then $\frac{|A|}{|B|}=$_______
Solution:
Given:
$A$ and $B$ are non-singular square matrices of order $n$.
$A=k B$
$A=k B$
Taking determinant on both sides, we get
$\Rightarrow|A|=|k B|$
$\Rightarrow|A|=k^{n}|B| \quad(\because$ Order of $B$ is $n \times n)$
$\Rightarrow \frac{|A|}{|B|}=k^{n}$
Hence, $\frac{|A|}{|B|}=\underline{k}^{n}$.
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