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Proof About Matrices


Date: 06/02/99 at 00:46:48
From: Ryuhei Hagiwara
Subject: Matrices

How do I prove that in two 2 x 2 matrices, A and B, AB - BA will never 
be the multiplication identity matrix?

Date: 06/02/99 at 12:17:24
From: Doctor Rob
Subject: Re: Matrices

One way is to show that the main diagonal entries of the result are 
the negatives of each other.

Another way of saying this is that the trace of the result is zero, 
because tr(X-Y) = tr(X) - tr(Y) and tr(AB) = tr(BA).

- Doctor Rob, The Math Forum
  http://mathforum.org/dr.math/

Associated Topics:
High School Linear Algebra

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