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## Homework Statement

Prove that for any

*m x s*matrix A and any

*s x n*matrix B it holds that:

rank(A) + rank(B) - s

is less or equal to:

rank(AB)

## The Attempt at a Solution

Obviously, the following are true:

- rank(A) is less or equal to s,

- rank(B) is less or equal to s,

- rank(AB) is less or equal to both rank(A) and rank(B).

So it is possible to prove:

rank(A) + rank(B) - 2s is less or equal to rank(AB).

Really don't know what can be done next. Thanks for any help on this.