# prove that if A^2=A...

#### skoker

##### New member
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
let A be a non singular matrix. then $$A^2=A, \quad A^{-1}A^2=A^{-1}A, \quad IA=I, \quad A=I$$
Right

therefore $$A^2=A.$$
Why do you write this? $A^2=A$ just by hypothesis.

#### skoker

##### New member
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
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