Question

If $A_{3\ast 3}$ and det $A=5$ then det (adj $A$) =

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

Answer 1

The correct option is B $25$

If A is a nth order square matrix, then
$det\left(adjA\right)$
$=(detA{)}^{n-1}$
Hence 'n' is 3 and detA is 5.
Substituting in the above formula, gives us
$det\left(adjA\right)=(detA{)}^{3-1}$
$=(detA{)}^2$
$=(5{)}^2$
$=25$