Minor and cofactor of a matrix

In linear algebra, a minor of a matrix is the determinant of some smaller square matrix, cut down from by removing one or more of its rows and columns.

If A is a square matrix, then the minor of the entry in the - th row and - th column is the determinant of the sub-matrix formed by deleting the -th row and - th column. This number is often denoted . The cofactor is obtained by multiplying the minor by .

Example:

To compute the minor and the cofactor , we find the determinant of the above matrix with row 2 and column 3 removed.

So the cofactor of the (2,3) entry is: