Cofactor

To find the cofactor of a matrix, first, calculate the matrix of minors. After the matrix of minors is known, multiply every element, (i, j), in the matrix by -1 to the i + j power. The value of Add -1(i+j) power forms a convenient checkerboard pattern with + always being at the top left:

Figure 3.7: A checkerboard pattern of -1 to the i + j power

The preceding diagram shows the checkerboard pattern that Add -1(i+j) creates. Notice how the pattern always starts with a positive element in the top left.