Building the cofactor matrix
The cofactor matrix can easily be built once cofactors of all the elements are calculated.
Now let’s build the cofactor matrix of the following matrix.
\[\Large
A =
\begin{bmatrix}
2 & 1 & 4 \\
1 & 6 & 3 \\
5 & 2 & 2
\end{bmatrix}
\]
For the simplicity we are not going to calculate cofactors of all nine elements in this page, refer to the previous page to learn how to calculate cofactors.
When cofactors of all the elements are calculated, place the cofactors in their distinct places to get the cofactor matrix.
\[\Large
C =
\begin{bmatrix}
C_{11} & C_{12} & C_{13} \\
C_{21} & C_{22} & C_{23} \\
C_{31} & C_{32} & C_{33}
\end{bmatrix}
\]
Following is the cofactor matrix of our above example matrix.
\[\Large
\mathbf{
A =
\begin{bmatrix}
6 & 13 & -28 \\
6 & -16 & 1 \\
-21 & -2 & 11
\end{bmatrix}
}
\]