Invertibility Criteria and Inverse Calculation

This lecture covers the first criterion for matrix invertibility, stating that a matrix is invertible if and only if the homogeneous system AX=0 has a unique solution. The proof involves elementary matrices and leads to the reduced row-echelon form of the matrix. The process of calculating the inverse of a matrix is demonstrated through examples, showing the application of elementary row operations to obtain the identity matrix. The lecture concludes with the concept of matrix invertibility and the product of elementary matrices.