two questions about row echelon forms

1)prove that the reduced row echelon form of an n by n matrix either is the identity matrix or contains at least one row of zeros

2)let the homogenius system Ax=0 whose augmented matrix is A/O be equivalent to R/0 where R is an equivalent matrix in reduced row echelon form.Let there be n unknowns and r non zero rows in R If r is smaller than n then the linear system A/O has infinite number of solutions. prove it