Mathematics Question from JEE Main 2025 · 3 April, Shift 2

Let $I$ be the identity matrix of order $3 \times 3$ and for the matrix $A = \begin{pmatrix} \lambda & 2 & 3 \\ 4 & 5 & 6 \\ 7 & -1 & 2 \end{pmatrix}$, $|A| = -1$. Let $B$ be the inverse of the matrix $\operatorname{adj}(A \cdot \operatorname{adj}(A^2))$. Then $|(\lambda B + I)|$ is equal to _____