| Theorem |
|
A determinant of a matrix A equals the sum of the products of elements of any row of A and the corresponding cofactors: |
Proof: By the definition,
.
We can combine similar terms to represent the above sum in the form
,
where
Note that
Therefore,
.
In this formula
is the minor of the element ai,j.
Thus, Ai,j is the cofactor of the element ai,j.
