Let $A$ be a $3\times 3$ matrix with $\det A=7$. Find $\det (\mathrm{adj}A)$.

Step-by-step solution

1. Recall $\mathrm{adj}A$ has determinant $\det A^{,n-1}$ for an $n\times n$ matrix.
2. Here $n=3$, so $\det (\mathrm{adj}A)=\det A^{,3-1}=\det A^{,2}$.
3. Substitute $\det A=7$: $\det (\mathrm{adj}A)=7^2=49$.

Concept tested: Determinant of adjoint matrix

Published 16 October 2026 · How this solution was prepared and checked