Definition (Adjoint)

Given some matrix $A\in M_{n}(\mathbb{R})$ we have that the adjoint of $A$ is $$\text{adj}(A)=F^{\top}$$where $$F_{ij}=(-1)^{i+j}\text{det}(\hat{A}_{ij})$$where $\hat{A}_{ij}$ is the $(n-1)\times(n-1)$ matrix obtained by removing the $i$th row and $j$th column of $A$.