LA44 A invertible iff Det(A) not zero; Det(AB) = Det(A) Det(B)

We prove (1) a matrix is invertible if and only if its #determinant is not zero; (2) Det(AB) = Det(A)Det(B) for square matrices A & B; (3) Det(A^{-1}) = 1/Det(A).#linearalgebra #matrices #matrixalgebra #determinants Subscribe ‪@Shahriari‬ for math videos for college. 00:00 Introduction & Lecture Plan 00:52 Definition of Determinant (   • LA41 Determinants: Definition via Elementa...  ) 01:56 Elementary row operations (   • LA17 Elementary Row Operations, Reduced Ro...  ) 02:36 Elementary row operations & Determinants (   • LA43 Determinants & Elementary Row Operations  ) 03:03 Theorem & Proof: A invertible if and only if Det(A) is not zero 04:57 Elementary Matrices (   • LA31 Elementary Matrices and their inverses  ) 06:20 Determinant of Elementary Matrices 07:07 Lemma & Proof: Det(EA) = Det(E)Det(A) if E is an elementary matrix 08:21 Proving a generalization of the Lemma 09:21 Version 2 of Proof: A invertible iff Det(A) nonzero 10:07 Main Theorem & Proof: Det(AB) = Det(A)Det(B) 12:26 Theorem & Proof: Determinant of the inverse of A is 1/Det(A) A series of lectures on Determinants of Matrices. LA41 Definition of Determinant    • LA41 Determinants: Definition via Elementa...   LA42 Determinant is Multi-linear and Alternating    • LA42 Determinant is Multi-linear and Alter...   LA43 Determinants & Elementary Row Operations    • LA43 Determinants & Elementary Row Operations   LA44 A invertible iff Det(A) nonzero; Det(AB) = Det(A)Det(B)    • LA44 A invertible iff Det(A) not zero; Det...   LA45 What is Cofactor Expansion? (   • LA45 Determinants: What is Cofactor Expans...  ) This is also a video in a series of lectures on linear algebra. The series is a rigorous treatment meant for students with no prior exposure to linear algebra. In this full undergraduate course in linear algebra, general vector spaces and linear transformations are emphasized. For an annotated list of available Linear Algebra videos see https://pomona.box.com/s/oahafa797tj5... Linear Algebra YouTube Playlist:   • Linear Algebra, a Retro introduction   Shahriar Shahriari is the William Polk Russell Professor of Mathematics at Pomona College in Claremont, CA USA Shahriari is a 2015 winner of the Mathematical Association of America's Haimo Award for Distinguished Teaching of Mathematics, and six time winner of Pomona College's Wig teaching award.