if A is an invertible matrix of order 3 and |A|=5 the find the value of |adjA|

Consider,
$$\begin{gathered} A^{-1}=\frac{adj\left(A\right)}{\left|A\right|} \\ \Rightarrow A\times A^{-1}=A\times \frac{adj\left(A\right)}{\left|A\right|} \\ \Rightarrow I=A\times \frac{adj\left(A\right)}{\left|A\right|} \end{gathered}$$

Since, A is invertible

$$\begin{gathered} \Rightarrow I\times \left|A\right|=A\times adj\left(A\right) \\ \Rightarrow \left|I\times \left|A\right|\right|=\left|A\times adj\left(A\right)\right| \end{gathered}$$

$\Rightarrow {\left|A\right|}^3=\left|A\right|\times \left|adj\left(A\right)\right|$ [Since, A is an invertible matrix of order 3]

$$\begin{gathered} \Rightarrow \left|adj\left(A\right)\right|={\left|A\right|}^2 \\ \Rightarrow \left|adj\left(A\right)\right|={\left(5\right)}^2=25 \end{gathered}$$