Zero matrix

In mathematics, particularly linear algebra, a zero matrix or null matrix is a matrix all of whose entries are zero. It also serves as the additive identity of the additive group of ${\displaystyle m\times n}$ matrices, and is denoted by the symbol ${\displaystyle O}$ or ${\displaystyle 0}$ followed by subscripts corresponding to the dimension of the matrix as the context sees fit.^[1][2][3] Some examples of zero matrices are

${\displaystyle 0_{1,1}={\begin{bmatrix}0\end{bmatrix}},\ 0_{2,2}={\begin{bmatrix}0&0\\0&0\end{bmatrix}},\ 0_{2,3}={\begin{bmatrix}0&0&0\\0&0&0\end{bmatrix}}.\ }$