Suppose $m$ and $n$ are positive integers, $m \neq n$, and $A$ is an $m \times n$ matrix with real entires. Consider the following statements.
- $\operatorname{rank}\left(A A^{T}\right)=\operatorname{rank}\left(A^{T} A\right)$
- $\operatorname{det}\left(A^{T} A\right)=\operatorname{det}\left(A A^{T}\right)$
- $\operatorname{Trace}\left(A A^{T}\right)=\operatorname{Trace}\left(A^{T} A\right)$
Which of the above statements is true for all such $A?$
- Only (i)
- Only (ii)
- Only (iii)
- (i) and (iii)
- None of them