True False Problem

Enter T or F depending on whether the statement is true or false. $($You must enter T or F $--$ True and False will not work.$)$ Note you only have $5$ attempts on this problem.

If a matrix is in reduced$-$row echelon form, then the first nonzero entry in each row is a $1$ and has $0\text{'}$s below it$.$

If an augmented matrix in reduced row$-$echelon form has $2$ rows and $3$ columns $($to the left of the vertical bar$),$ then the system has infinitely many solutions.

If the bottom row of a matrix in reduced row$-$echelon form contains all $0\text{'}$s$,$ then the system has infinitely many solutions.