Question

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

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

Answer 1

The correct option is C $27|A|$

If $A$ is a matrix then $3A$ is obtained by multiplying 3 with each element of the matrix therefore taking $3$ common from each row (or column), we get
$|3A|=(3\times 3\times 3)|A|=27|A|$