Invertible Matrices: Definitions and Properties

This lecture covers the definitions and properties of invertible matrices, focusing on the characterization of nxn invertible matrices. Starting with the definition of invertibility, the instructor explains the conditions for a matrix to be invertible, such as the existence of the inverse and the product of matrices. The lecture also delves into determinants, linear systems, and the uniqueness of solutions. Through examples and demonstrations, the lecture illustrates how to determine if a matrix is invertible and the implications of invertibility in linear algebra.