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Let $A$ be a $4 \times 3$ real matrix with rank $2$. Which one of the following statement is TRUE?

  1. Rank of $A^{T} A$ is less than $2$.
  2. Rank of $A^{T} A$ is equal to $2$.
  3. Rank of $A^{T} A$ is greater than $2$.
  4. Rank of $A^{T} A$ can be any number between $1$ and $3$.
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