Zero matrix

As the name suggests, a ‘zero’ matrix is just a matrix where all the elements are zero.

Order of a zero matrix

We can have zero matrices of any order (dimensions), for example:

• A zero matrix:
• A zero matrix:
• A zero matrix:
• A zero matrix:
• A zero matrix:
• A zero matrix:

Identity matrix

A zero matrix is the identity matrix for addition. That’s because, if we add a zero matrix to any other matrix of the same order, we get that same matrix back.

For example, if we have the matrix and the zero matrix , then:

If you want some algebraic proof:

• Let and , then:

Multiplication with a zero matrix

If we multiply any matrix by a zero matrix of compatible dimensions, we get a zero matrix as the result.

The proof of this for some matrices is as follows:

• Let and , then: