How to compute the matrix of minors of this matrix

$$ \begin{bmatrix} a & b & c\\ d & e & f\\ g & h & i \end{bmatrix} $$ To find the minor of a matrix, we take the determinant of each smaller matrix, obtained by deleting the corresponding rows and columns of each element in the matrix. Since in the large matrices, there are many rows and columns with multiple elements, therefore we can make many minors of those matrices. We label these minors according to the row and column they belong to. Each element in the square matrix has its minor. $$ M_{11}= \begin{bmatrix} e & f\\ h & i \end{bmatrix} =(ei-fh), $$ $$ M_{12}= \begin{bmatrix} d & f\\ g & i \end{bmatrix} =(di-fg), $$ $$ M_{13}= \begin{bmatrix} d & e\\ g & h \end{bmatrix} =(dh-eg), $$ $$ M_{21}= \begin{bmatrix} b & c\\ h & i \end{bmatrix} =(bi-ch), $$ $$ M_{22}= \begin{bmatrix} a & c\\ g & i \end{bmatrix} =(ai-cg), $$ $$ M_{23}= \begin{bmatrix} a & b\\ g & h \end{bmatrix} =(ah-bg), $$ $$ M_{31}= \begin{bmatrix} b & c\\ e & f \end{bmatrix} =(bf-ce), $$ $$ M_{32}= \begin{bmatrix} a & c\\ d & f \end{bmatrix} =(af-cd), $$ $$ M_{33}= \begin{bmatrix} a & b\\ d & e \end{bmatrix} =(ae-bd), $$ Therefore, $$ M= \begin{pmatrix} M_{11} & M_{11} & M_{11}\\ M_{21} & M_{22} & M_{23}\\ M_{31} & M_{32} & M_{33}\\ \end{pmatrix} = \begin{pmatrix} \begin{bmatrix} e & f\\ h & i \end{bmatrix} & \begin{bmatrix} d & f\\ g & i \end{bmatrix} & \begin{bmatrix} d & e\\ g & h \end{bmatrix} \\ \begin{bmatrix} b & c\\ h & i \end{bmatrix} & \begin{bmatrix} a & c\\ g & i \end{bmatrix} & \begin{bmatrix} a & b\\ g & h \end{bmatrix} \\ \begin{bmatrix} b & c\\ e & f \end{bmatrix} & \begin{bmatrix} a & c\\ d & f \end{bmatrix} & \begin{bmatrix} a & b\\ d & e \end{bmatrix} \end{pmatrix} $$ The cofactor of the element is denoted as $C_{ij}$. If the minor of the element is $M_{ij}$, therefore, the cofactor of element would be $C_{ij}=(-1)^{i+j}M_{ij}$. $$ C= \begin{pmatrix} (-1)^{1+1}M_{11} & (-1)^{1+2}M_{12} & (-1)^{1+3}M_{13} \\ (-1)^{2+1}M_{21} & (-1)^{2+2}M_{22} & (-1)^{2+3}M_{23} \\ (-1)^{3+1}M_{31} & (-1)^{3+2}M_{32} & (-1)^{3+3}M_{33} \end{pmatrix} $$