Question

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

• A. $\pm 1$
• B. $\pm 1/5$
• C. $\pm 1/25$
• D. $\pm 5$

Answer 1

Answer: (B)

$A_{3\times 3}$ matrix $|5.\mathrm{AdjA}|=5$
$\Rightarrow 5^3|A{|}^2=5$
$\Rightarrow \left|A^2\right|=\frac{1}{5^2}$
$|A|=\pm \frac{1}{5}$