Zero matrix

Description

Let $R$ be a ring and let $m, n \ge 0$ be integers. The $m \times n$ zero matrix over $R$ is the matrix $0_{m \times n}$ whose entries are all $0$. It is the identity element for matrix addition: $A + 0 = 0 + A = A$ for each $m \times n$ matrix $A$. For each matrix $B$ with $n$ rows, the product $0_{m \times n} B$ is a zero matrix.