Question: Let A be an m * n matrix with rank m and B be an n * p matrix with rank n. Determine the rank of AB. Justify your answer.

Attempt: I don't really know where to start off, but I have some things that might help me. I know that the rank of a matrix is equal to the number of linearly independent rows in it, and I also know that if A and B are two matrices, then rank(AB) <= rank(A) and also rank(AB) <= rank(B).