Finding the 4x4 Cofactor of a Covariant Metric Tensor g_{ik}

[Philosophaie]

If I have a 4x4 Covarient Metric Tensor $$g_{ik}$$.

I can find the determinant:

$$G = det(g_{ik})$$

How do I find the 4x4 Cofactor of g_ik?
$$G^{ik}$$

then $$g^{ik}=G^{ik}/G$$

 

[Bill_K]

This is just standard matrix inversion. Quoting from the Wikipedia page on "minors",

If A is a square matrix, then the minor of the entry in the i-th row and j-th column (also called the (i,j) minor, or a first minor[1]) is the determinant of the submatrix formed by deleting the i-th row and j-th column. This number is often denoted Mi,j. The (i,j) cofactor is obtained by multiplying the minor by (-1)^{i+j}.