It is given that A is an mxn matrix, and B is an nxn, invertible matrix. I want to show that Im(A) = Im(AB).

To show that they are equivalent, I went the road of showing that they must be subsets of each other.

Im(AB) = {ABX | X in R^n}

let M = ABX

M = (AB)X

M is in Im(A) due to AB is any mxn matrix?

I'm stuck here now and any help would be appreciated.

Thanks!