Question

If $A$ is a $3\times 3$ matrix and $detA=5,$ then $det\left(adjA\right)$ is equal to

• A. $5$
• B. $25$
• C. $125$
• D. $\frac{1}{5}$

Answer 1

The correct option is B $25$

We know that, if $A$ is a $n^{th}$ order square matrix, then
$det\left(adjA\right)=(detA{)}^{n-1}$
Here, $n=3$ and $detA=5$
$\therefore det\left(adjA\right)=(detA{)}^{3-1}=(detA{)}^2$
$=5^2$
$=25$