Answer on Linear Algebra Question for Matthew Lind
that BA=1_n (identity matrix of size N) iff
If M<N then N<=rank(A)<M and so there is no left inverse.
If M>N then only possible case is rank(A)=rank(B)=N.
So, M by N matrix A has left inverse iff N<M and rank(A)=N.
So, M by N matrix A has right inverse iff N>M and rank(A)=M.
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