Zero Matrix is a type of matrix whose elements are equal to zero. Zero matrix is also known as null matrix. It is generally denoted by capital letter ‘O‘.
A matrix O = [xij] is said to be null matrix or zero matrix if xij = 0 for all values of ‘i‘ and ‘j‘. This matrix need not to be a square matrix.
Null matrix examples
The example of a null matrix of order 3 (or matrix size is 3 x 3) is given below.
\[O=\begin{bmatrix} 0 &0 &0 \\ 0& 0 &0 \\ 0&0 & 0 \end{bmatrix}\]
The example of a zero matrix of order 2 (or matrix size is 2 x 2) is given below.
\[O=\begin{bmatrix} 0 &0 \\ 0& 0 \end{bmatrix}\]
The example of a null matrix of size 3 x 1 is given below.
\[O=\begin{bmatrix} 0\\ 0\\ 0 \end{bmatrix}\]
The example of a zero matrix of size 2 x 3 is given below.
\[\begin{bmatrix} 0 & 0 & 0 \\ 0 & 0 & 0 \end{bmatrix}\]
Null matrix properties
Let P be a matrix and O is a null matrix of the same size as of matrix P.
1. P + O = O + P = P
2. P + (-P) = O
3. The determinant of a null matrix is 0 i.e. |O| = 0.
4. The rank of a null matrix or zero matrix is zero.
