Def:         Mij ≡ minor matrixij (of square matrix A) ≡ A with row i and column j deleted.

Ex:

                 

Tool:      One method of computing the determinant of matrix A involves minors for one row or one column of a matrix.

Ex:

                 

Using minors of row one, we have

We apply the determinant calculation recursively to the 2 x 2 matrices (using the minors of the top row of each one):

Note:      The power of −1 for the new, smaller minor matrices is determined by the index within that minor matrix rather than the index within the original matrix.

Note:      We may use minors for a row or column containing many entries equal to zero to reduce calculations.