# What is a zero matrix? Definition and examples

What is a zero matrix? A zero matrix, also called null matrix, is a matrix where all elements of the matrix are equal to 0.

$$O = [O_{m × n}] = \begin{bmatrix} 0 & 0 & 0 & . . . & 0\\ 0 & 0 & 0 & . . . & 0\\ 0 & 0 & 0 & . . . & 0\\ . & . & . & & .\\ . & . & . & & .\\ . & . & . & & .\\ 0 & 0 & 0 & . . . & 0\\ \end{bmatrix}$$

## Here are a few more examples of zero matrices

$$O = [O_{2 × 2}] = \begin{bmatrix} 0 & 0\\ 0 & 0\\ \end{bmatrix}$$
$$O = [O_{3 × 3}] = \begin{bmatrix} 0 & 0 & 0\\ 0 & 0 & 0\\ 0 & 0 & 0\\ \end{bmatrix}$$
$$O = [O_{3 × 2}] = \begin{bmatrix} 0 & 0\\ 0 & 0\\ 0 & 0\\ \end{bmatrix}$$