Question

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

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

Answer 1

Answer: (A)

Order of $A$ is $3\times 3;|5.adjA|=5$;
$|5(adjA)|=5\Rightarrow (5{)}^3|Adj.A|=5$
$\Rightarrow (5{)}^2|A{|}^{\beta -1}=1$
$\Rightarrow |A{|}^2=\frac{1}{25}$
$\Rightarrow |A|=\pm \frac{1}{5}$