Determinant of a Product

This lecture covers the determinant of a product of matrices, stating that the determinant of the product of two matrices is equal to the product of their determinants. The proof involves the invertibility criterion, showing that if one of the matrices is not invertible, then the product is also not invertible. Additionally, two corollaries are presented: the determinant of the inverse of an invertible matrix is equal to the inverse of the determinant, and the determinants of similar matrices are equal. The lecture also discusses the use of elementary matrices in determining the determinant of a product.