This lecture covers the definition of the determinant of a matrix, including recursive definitions for 1x1 and 2x2 matrices, as well as the general formula for nxn matrices. Examples are provided to illustrate the calculation of determinants using the rule of Sarrus. The rule of Sarrus is explained as a method to calculate the determinant of a 3x3 matrix by using a specific pattern of elements. The lecture concludes with additional examples demonstrating the application of the rule of Sarrus in finding determinants.