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Show that for matrices A and B, det(AB) = det(BA) = det(A) det(B). Solution Let C = AB, then Cij = AikBkj and from Eq 2.
Posted: Wed May 04, 2022 10:34 am
by answerhappygod
- Show That For Matrices A And B Det Ab Det Ba Det A Det B Solution Let C Ab Then Cij Aikbkj And From Eq 2 1 (46.41 KiB) Viewed 47 times
Show that for matrices A and B, det(AB) = det(BA) = det(A) det(B). Solution Let C = AB, then Cij = AikBkj and from Eq 2.42 det e Eijk Cil Cj2Ck3 = EijkAiq Bq1AjmBm2 Akn Bn3 EijkAiq AjmAkn Bq1 11 Bm2 Bn3. But from Eq 2.43 EijkAiq AjmAkn = &qmn det A, so now Essential Mathematics det C = det AB = EqmnBq1Bm2Bn3 det A = det A det B. By a direct interchange of A and B, det .AB = det B.A. 23