Tuesday, 11 April 2017

matrices - Proof for linear algebra theorem

I want to prove that if AB=cI for some matrices A, B and number c, then AB=BA.
I start my proof with c0. then, A and B are invertible, And BA=B(cB1)=cBB1=cI=AB.
What about c=0?
I guess it's true, but i'm not sure. If I true for c=0, what is the proof? If It's not, what is the contradiction example?
Thank you.

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