ThmDex – An index of mathematical definitions, results, and conjectures.
Expression for a real matrix inverse in terms of adjugate
Formulation 0
Let $A \in \mathbb{R}^{N \times N}$ be a D6160: Real square matrix such that
(i) \begin{equation} \text{det} A \neq 0 \end{equation}
(ii) $A^{-1}$ is an D2089: Inverse matrix for $A$
Then \begin{equation} A^{-1} = \frac{1}{\text{Det} A} \text{Adj} A \end{equation}
Proofs
Proof 0
Let $A \in \mathbb{R}^{N \times N}$ be a D6160: Real square matrix such that
(i) \begin{equation} \text{det} A \neq 0 \end{equation}
(ii) $A^{-1}$ is an D2089: Inverse matrix for $A$