Question

If $A$ is a $3\times 3$ matrix such that $|5\cdot adjA|=5,$ then $|A|$ is equal to

• A. $\pm \frac{1}{5}$
• B. $\pm 5$
• C. $\pm 1$
• D. $\pm \frac{1}{25}$

Answer 1

The correct option is A $\pm \frac{1}{5}$

$|5\cdot adjA|=55^3|adjA|=5|adjA|=\frac{1}{25}|A{|}^{3-1}=\frac{1}{25}|A|=\pm \frac{1}{5}$