JEE Main 2022 · 27 Jun · Shift 1, Mathematics question 23

Identity. For $3\times3$, $\operatorname{adj}(\operatorname{adj}A)=|A|A$, so $\det=|A|^3\cdot|A|=|A|^4$.

Given matrix. $14\begin{pmatrix}1&2&-1\\-1&1&2\\2&-1&1\end{pmatrix}$, whose determinant is $14^3\times14=14^4$.

So $|A|=14$.

Answer: 14