What is a Zero Matrix (Null Matrix)?

A zero matrix, or null matrix, is a matrix whose all elements are zeros. As a null matrix has all zeros as its elements, it is referred to as a zero matrix. A zero matrix can be a square matrix, or it can also have an unequal number of rows and columns.

A zero matrix is represented as “O.” If we add a zero matrix to another matrix A of the same order, then the resultant matrix is A. So, a zero matrix is known as the additive identity of that particular matrix. The matrix given below represents a zero matrix of order “m by n.”

[Tex]O m×n = \left[\begin{array}{cccccc} 0 & 0 & . & . & . & 0\\ 0 & 0 & . & . & . & 0\\ . & . & . &  &  & .\\ . & . &  & . &  & .\\ 0 & 0 & . & . & . & 0 \end{array}\right]_{m\times n}[/Tex]

A zero matrix, or null matrix, is a matrix whose all elements are zeros. A matrix is defined as a rectangular array of numbers that are arranged in rows and columns. The size of a matrix can be determined by the number of rows and columns in it. A matrix is said to be an “m by n” matrix when it has “m” rows and “n” columns and is written as an “m × n” matrix. For example, the matrix given below is a “2 × 3” matrix, i.e., a matrix that has two rows and three columns. We have different types of matrices, such as rectangular matrices, square matrices, triangular matrices, symmetric matrices, etc.

[Tex]A = \left[\begin{array}{ccc} 1 & -5 & 3\\ 7 & 8 & 4 \end{array}\right][/Tex]