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prove that if A^2=A...

skoker

New member
Feb 2, 2012
14
i have a simple proof is this correct?

prove that if \(A^2=A\), then either A=I or A is singular.

let A be a non singular matrix. then \(A^2=A, \quad A^{-1}A^2=A^{-1}A, \quad IA=I, \quad A=I\) therefore \(A^2=A.\)
 

Fernando Revilla

Well-known member
MHB Math Helper
Jan 29, 2012
661

skoker

New member
Feb 2, 2012
14
Right
Why do you write this? $A^2=A$ just by hypothesis.
i suppose that is redundant or unnecessary. i was not sure if it needs a conclusion with the 'therefore'.
 

CaptainBlack

Well-known member
Jan 26, 2012
890
i suppose that is redundant or unnecessary. i was not sure if it needs a conclusion with the 'therefore'.
The therfore should go before the \(A=I\) and you should stop at that point.

CB