Question

Let $A$ be a square matrix of order $3\times 3$ then $\left|KA\right|$ is equal to

• A. $K\left|A\right|$
• B. $K^2\left|A\right|$
• C. $K^3\left|A\right|$
• D. $3\left|KA\right|$

Answer 1

Answer: (C)

$K^3\left|A\right|$

$Usingpropertiesofdeterminant$

$|kA|=k^n|A|$

$wherenisorderdeterminant$

$SincegivenmatrixAhasorder3$

$hence\left|kA\right|=k^3\left|A\right|$