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Current Location > Math Formulas > Linear Algebra > Definition of Zero Matrix

Definition of Zero Matrix

A matrix is known as a zero or null matrix if all of its elements are zero.

Examples:

etc. are all zero matrices.

If you add the m×n zero matrix to another m×n matrix A, you get A:

In symbols, if 0 is a zero matrix and A is a matrix of the same size, then
A + 0 = A and 0 + A = A

A zero matrix is said to be an identity element for matrix addition. A zero matrix serves many of the same functions in matrix arithmetic that 0 does in regular arithmetic.

Example 1: What is the resultant when we add the given matrix to the null matrix?

Solution:
We know that A + 0 = A
Therefore,

Example 2: Show that the sum of matrix Q and its additive inverse is a zero matrix.

Solution:
Its additive inverse is given by

Now

Hence the sum of matrix Q and its additive inverse is a zero matrix.

Example 3: What is the resultant when we add the given matrix A to the null matrix?

Solution:
We know that A + 0 = A
Therefore,