### Video Summary:

Subscript notation for the matrix A
The row 1, column 1 element is a11; the row 2, column 3 element is a23; and, in general, the row i, column j element is aij. Associated with every square matrix is a real number called the determinant of A. In this text, we use det A. A method for calculating 3 × 3 determinants is found by re-arranging and factoring this formula.
Each of the quantities in parentheses represents the determinant of a 2 × 2 matrix that is part of the
3 × 3 matrix remaining when the row and column of the multiplier are eliminated.