Minor and Cofactor
An element, aij, to the value of the determinant of order n − 1, obtained by deleting the row i and the column j in the matrix is called a minor.
The cofactor of the element aij is its minor prefixing:
The + sign if i+j is even.
The − sign if i+j is odd.
The value of a determinant is equal to the sum of the products of the elements of a line by its corresponding cofactors:
= 3(8+5) - 2(0-10) + 1(0+4) = 39 + 20 + 4 = 63