The determinant of an invertible square real matrix is the multiplicative inverse of the determinant of the matrix.
Let $A \in \R ^{n \times n}$ be invertible. We want to show that \[ \det (A^{-1}) = (det(A))^{-1}. \]
\[ \det (A^{-1}) = (det(A))^{-1}. \]