# Whether the below matrices are in row-echelon form / reduced row-echelon form

I would like to ask whether the following matrix is a row echelon matrix (and reduced row-echelon matrix).
The below are $$1 \times 1$$ matrices.
(a) $$\begin{pmatrix} 0\end{pmatrix}$$
(b) $$\begin{pmatrix} 1\end{pmatrix}$$
(c) $$\begin{pmatrix} 2\end{pmatrix}$$

The below are $$n\times1$$ matrices, where $$n\in \mathbb{R}$$ and $$n \geq 2$$
(d) $$\begin{pmatrix} 0 & 0 & \cdots & 0\end{pmatrix}$$

Here are my opinions. I would like for my opinions be confirmed (or to be countered if mine is wrong):
(a) It is a row echelon form and reduced row echelon form.
(b) It is a row echelon form and reduced row echelon form. The entry $$1$$ is the leading one.
(c) It is a row echelon form, but it is not a reduced row echelon form, since there is no leading $$1$$ before $$2$$
(d) It is a row echelon form and reduced echelon form. \

(For (d), it is inspired by " Is a $1 \times n$ matrix already in echelon form? ".)

According to Linear Algebra and Its Applications by Lay, p. 13

A rectangular matrix is in echelon form (or row echelon form) if it has the following three properties:

1. All nonzero rows are above any rows of all zeros.
2. Each leading entry of a row is in a column to the right of the leading entry of the row above it.
3. All entries in a column below a leading entry are zeros.

If a matrix in echelon form satisfies the following additional conditions, then it is in reduced echelon form (or reduced row echelon form):

1. The leading entry in each nonzero row is 1.
2. Each leading 1 is the only nonzero entry in its column.

A leading entry of a row refers to the leftmost nonzero entry (in a nonzero row).

So, yes you are correct based on the above.