1. Let's start by defining the problem: Given a square matrix $A$, we want to find its cofactor matrix, adjoint (also called adjugate) matrix, and inverse matrix. 2. The cofactor matrix is formed by calculating the cofactor of each element in $A$. The cofactor $C_{ij}$ of element $a_{ij}$ is given by: $$C_{ij} = (-1)^{i+j} M_{ij}$$ where $M_{ij}$ is the determinant of the submatrix formed by deleting the $i$-th row and $j$-th column from $A$. 3. The adjoint (adjugate) matrix $\text{adj}(A)$ is the transpose of the cofactor matrix: $$\text{adj}(A) = (C_{ij})^T$$ 4. The inverse of $A$, if it exists (i.e., if $\det(A) \neq 0$), is given by: $$A^{-1} = \frac{1}{\det(A)} \text{adj}(A)$$ 5. To proceed, please provide the specific matrix $A$ you want to analyze so I can compute the cofactor matrix, adjoint, and inverse with whole values.