What is a cofactor of a determinant?

The cofactor is the signed minor of a determinant, used to evaluate the determinant. You take the minor of the element - call that element aij - and if i + j is even, the cofactor is the minor

• otherwise, it's the opposite of the minor. Thus, take the matrix,

remove the row and column the element is in, and if the sum of the row number and column number is even, then there's your cofactor; otherwise, it's the additive inverse. For example, the cofactor of a34 is the determinant of the same matrix with the 3rd row and 4th column removed, and then you take the opposite (additive inverse or negative), because 3 + 4 = 7 is odd.