# Is the zero matrix in reduced row echelon form?

Is this matrix in reduced row echelon form? $3\times3$ matrix is:

0 0 0
0 0 0
0 0 0


I can say for other matrices but this one without 1s confuses me. Are $1$s optional in reduced row echelon form? I think they aren't. What do you think?

• What do you mean by "Are ones optional"? – 5xum Nov 17 '15 at 22:30
• @5xum Typically, RREF contains some 1s. The OP wants to know if it has to be that way. – user147263 Nov 17 '15 at 22:32
• I mean to say, are 1s that appear in reduced row echelon form optional? Will it be still reduced row echelon if I have not a single 1 in matrix. – user4904589 Nov 17 '15 at 22:33

In a logical sense, yes. The zero matrix is vacuously in RREF as it satisfies:

1. All zero rows are at the bottom of the matrix

2. The leading entry of each nonzero row subsequently to the first is right of the leading entry of the preceding row.

3. The leading entry in any nonzero row is a 1.

4. All entries in the column above and below a leading 1 are zero.