Spaces of matrices and projective spaces

Question

Consider $\mathbb{C}^8$ i.e. 8 copies of the field of the complex numbers. I want to identify it with the set of matrices 2x4 $(z_{00},z_{01},z_{02},z_{03},z_{10},z_{11},z_{12},z_{13})$ now i have to consider the subset $X$ of $\mathbb{P}^7$ of matrices of rank 1. My question is: can I consider $X$ as the segre embedding of $\mathbb{P}^3 \times \mathbb{P}^3$ in $\mathbb{P}^7$? Since the condition to define $X$ is that 2x2 minors are zero i.e. $z_{0i}z_{1j}-z_{0j}z_{1i}=0$ and it seems the definition of the Segre variety. Thanks for the answer!