JEE Main 2022 (Online) 27th June Morning ShiftQuestion 1
The positive value of the determinant of the matrix $A$, whose $\operatorname{Adj}(\operatorname{Adj}(A))=\begin{pmatrix}14&28&-14\\-14&14&28\\28&-14&14\end{pmatrix}$, is $\_\_\_\_\_\_$ .
Determinant
Answer$14$
Solution
For $3\times3$, $\operatorname{Adj}(\operatorname{Adj}A)=|A|A$, so its determinant is $|A|^4$. Given matrix has determinant $38416=14^4$, so $|A|=\pm14$. Positive value: $14$.