I found a discrepancy between the book on tensors I'm reading (that is very old) with a post here, namely "https://math.stackexchange.com/questions/4085719/a-doubt-on-the-derivative-of-a-determinant".
In this post it is said that:
i.e. the derivative of metric determinant are given by $A^ab$, the elements of cofactor matrix of $g_ab$.
On the other hand, in McConnell`s Tensor Analysis it is said:
And now the cofactor has its row and column inverted in relation to the element the determinant is derived. Which one is right?
Or perhaps the autor defines cofactor in a different way than we do? If that is the case, than the following definition should also be inverted (here delta is the Kroenecker delta):
