The reduced row echelon form of a system of linear equations in $x$ and $y$ or in $x,y$ and $z$ is given. For each system, determine whether it has a unique solution $($in this case, find the solution$),$ infinitely many solutions, or no solutions.

$1.$

$\left[\begin{array}{cccc}1& 0& 0& 0\\ 0& 1& 0& 0\\ 0& 0& 0& 1\end{array}\right]$

A$.$ Unique solution: $x=0,y=0$

B$.$ Unique solution: $x=0,y=0,z=1$

C$.$ Infinitely many solutions

D$.$ Unique solution: $x=0,y=0,z=0$

E$.$ No solutions

F$.$ None of the above