The minor is the determinant of the matrix constructed by removing the row and column of a particular element. Thus, the minor of a34 is the determinant of the matrix which has all the same rows and columns, except for the 3rd row and 4th column.
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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.
relationship between determinant and adjoint
The resulting determinate is the negative, or opposite, of the original determinant.
A determinant is defined only for square matrices, so a 2x3 matrix does not have a determinant.Determinants are defined only for square matrices, so a 2x3 matrix does not have a determinant.
The determinant will change sign.