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# Definition of 0 matrix

Put content here.**Definition:** The **zero matrix** (or **null matrix**), denoted by $0$ or $0_{m \times n}$, is the $m \times n$ matrix in which every entry is zero:
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$$0_{m \times n} = \begin{pmatrix} 0 & 0 & \cdots & 0 \\ 0 & 0 & \cdots & 0 \\ \vdots & \vdots & \ddots & \vdots \\ 0 & 0 & \cdots & 0 \end{pmatrix}$$
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The zero matrix serves as the **additive identity** in the vector space of matrices: $A + 0 = A$ for any matrix $A$ of the same size.
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**Properties:**
- $A + 0 = A$ and $0 + A = 0$
- $A - A = 0$
- $0 \cdot A = 0$ and $A \cdot 0 = 0$
- $\text{rank}(0) = 0$
- $\det(0_{n \times n}) = 0$

# Parents

* Basic terminology and notation