If i am given a linear transformation D:A->A,that is followed by(adsbygoogle = window.adsbygoogle || []).push({});

A=ImD(+)kerD

and i am asked to prove that kerD^2=kerD and imD=imD^2.

instead of trying to work it out the hard way by showing that every element of KerD is an element of kerD^2 , both directions.

would it not be easier to just say that dimA=dimA and hence the two structures are isomorphic which means that KerD={0} and ImD=A.

same goes for D^2:A->A

KerD^2={0}

ImD^2=A

=> therefore KerD^2=KerD and ImD^2=ImD ?

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# Linear transformations

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