Matrix Proof

  • #1
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If A and B are n × n matrices, when does
(A + B)(A − B) = A^2 − B^2?

I guess I start out by expanding?

A^2 - BA-B^2+BA=0

Thus AB=BA in order for that to work?
 

Answers and Replies

  • #2
jbunniii
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If A and B are n × n matrices, when does
(A + B)(A − B) = A^2 − B^2?

I guess I start out by expanding?

A^2 - BA-B^2+BA=0

Thus AB=BA in order for that to work?

Correct.
 

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