A is m × n full rank matrix with m > n and $$I$$ is an identity matrix. Let matrix A’ = (ATA)-1AT, Then, which one of the following statement is TRUE? A. AA’ A = A B. (AA’)2 = A C. AA’A = $$I$$ D. AA’A = A’

The correct answer is $\boxed{\text{C}}$.

Let $A$ be an $m\times n$ full rank matrix with $m>n$. Then, $A^T A$ is an invertible matrix. Therefore, $(A^T A)^{-1}$ exists.

We know that $A^T A A = A^T$. Therefore,
\begin{align}
AA’ A &= A (A^T A)^{-1} A^T \
&= A (A^T A)^{-1} A \
&= I.
\end{align}

Option A is not true because $AA’ A$ is an identity matrix, not $A$.

Option B is not true because $(AA’)^2 = AA’ A A’ = AA’$.

Option D is not true because $AA’ A$ is an identity matrix, not $A’$.