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Im actually doing some systems theory and it requires some basic linear algebra stuff that I totally forgotten. Anyway:

according to my prof. :

For any matrix F. Im(BF) is contained in Im(B).

here is my question:

so Im(FB) is still in Im(B)? or is it true only when we multiply a matrix to the right of the origin matrix?

if Im(B) is in Im(T) and Im(AB) is in Im(T), is Im(A) in Im(T) as well? and is Im(BA) in Im(T). imagin that the dimention ab matrices are appropriate. and they are constant real matrices

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# Im(BF) in Im(B)?

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