Chapter 3 - Determinants - 3.2 Exercises - Page 178: 31

\begin{align*} & AA^{-1}=I \\ & \Rightarrow \det{AA^{-1}}=\det I=1 \\ & =(\det A) (\det{A^{-1}}) \\ & \Rightarrow\det A^{-1}=\frac{1}{\det A} \end{align*}

\begin{align*} & AA^{-1}=I \\ & \Rightarrow \det{AA^{-1}}=\det I=1 \\ & =(\det A) (\det{A^{-1}}) \\ & \Rightarrow\det A^{-1}=\frac{1}{\det A} \end{align*}