Let $\text{S}$ be the set of all $3 \times 3$ real matrices $\text{A} = ((a_{ij}))$ such that the matrix $ ((a^{3}_{ij}))$ has rank one. Define a set $\text{R} = \left \{ \text{rank(A)} : \text{A} \in \text{S}\right \}$. Then $\text{R}$ is equal to.
-
$\left \{ 1 \right \}$
-
$\left \{ 1, 2\right \}$
-
$\left \{ 1, 3 \right \}$
-
$\left \{ 1, 2, 3 \right \}$
