Question

Let A be a square matrix of order $3\times 3$, then $|kA|$ is equal to

• A. $k|A|$
• B. $k^2|A|$
• C. $k^3|A|$
• D. $3k|A|$

Answer 1

The correct option is C $k^3|A|$

If $A$ is a square matrix of order $n$ , then we can take $k$ common from each of the $n$ rows of $kA$

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

So, for a square matrix of of order $3$,

$|kA|=k^3|A|$