Question

If $A$ is any square matrix of order $3\times 3$ then $\left|3A\right|$ is equal to

• A. $3\left|A\right|$
• B. $\frac{1}{3}\left|A\right|$
• C. $27\left|A\right|$
• D. $9\left|A\right|$

Answer 1

The correct option is C $27\left|A\right|$

We know that: If A is a square matrix of order $n$ and its determinant is $|A|$

Then for any scaler $k$, $|kA|=k^n|A|$

Here $n$ is $3$, so $|3A|=3^3|A|=27|A|$