Question

Let $A$ be a square matrix of order $3\times 3$, then $|5A|=$

• A. $5|A|$
• B. $125|A|$
• C. $25|A|$
• D. $15|A|$

Answer 1

The correct option is B $125|A|$

We know, If $A$ is a square matrix of order $n$, then $|kA|=k^n|A|$, where $k$ is a scalar.
Given $A$ is a $3\times 3$ matrix.
$\therefore |5A|=5^3|A|=125|A|$