SOLUTION: Let A, B, and C be any nxn matrices. Prove that trace(ABC) = trace(CAB) = trace(BCA).
Algebra
->
Matrices-and-determiminant
-> SOLUTION: Let A, B, and C be any nxn matrices. Prove that trace(ABC) = trace(CAB) = trace(BCA).
Log On
Algebra: Matrices, determinant, Cramer rule
Section
Solvers
Solvers
Lessons
Lessons
Answers archive
Answers
Click here to see ALL problems on Matrices-and-determiminant
Question 1062029
:
Let A, B, and C be any nxn matrices. Prove that trace(ABC) = trace(CAB) = trace(BCA).
Answer by
ikleyn(52786)
(
Show Source
):
You can
put this solution on YOUR website!
.
Let A, B, and C be any nxn matrices. Prove that trace(ABC) = trace(CAB) = trace(BCA).
~~~~~~~~~~~~~~~~~~~~
For it, it is enough to prove trace(AB) = Trace(BA).
For this, see
http://math.stackexchange.com/questions/1099745/how-to-prove-tr-ab-tr-ba
http://math.stackexchange.com/questions/1099745/how-to-prove-tr-ab-tr-ba
