Is the product of two full column rank matrices full rank?

Question

If $A$ is a $T\times r$ matrix of full column rank, and B is another $T\times r$ matrix of full column rank. Then is the product ($r\times r$) matrix $A'B$ full rank? (If $T\rightarrow\infty$, I guess the question can be rephrased with regard to $A'B/T$.)