Matrix Product with Adjugate Matrix

Theorem
Let $$\mathbf{A} = \begin{bmatrix}a\end{bmatrix}_{n}$$ be an invertible square matrix of order $n$.

Let $$\mathbf{B} = \begin{bmatrix}b\end{bmatrix}_{n} = \mathbf{A}^{-1}$$ be the inverse of $$\mathbf{A}$$.

Then $$\mathbf{B}$$ is defined as:
 * $$b_{ij} = \frac {A_{ji}} {\det \mathbf{A}}$$

where $$A_{ji}$$ is the cofactor of $$a_{ji} \in \mathbf{A}$$.

Corollary
A square matrix is invertible iff its determinant is not zero.