Additive identity of a matrix example:

Let’s consider a matrix A of size m x n. The additive identity of this matrix, denoted as 0, is a matrix of the same size where all elements are equal to zero. For instance, if A is a 3 x 3 matrix, then the additive identity matrix would be:

0 0 0<br /> 0 0 0<br /> 0 0 0

If **A and B** are two matrixes of same order and **A + B = A = B + A **then the matrix B is called **additive identity of matrix A**.

**Additive identity**;

For any matrix A and zero matrix O of same order, is called** Additive identity of A.**

**Additive identity of a matrix example**:

**A + 0 = A = 0 + A**

PROOF:

Then

Hence, this proves the **A + O = A = O + A**

**Additive Inverse of Matrix A:**

If A and B are two matrices of same order such That

**A + B = O = B + A**

then A and B are called additive inverse of each other.

Additive inverse of any matrix A is obtained by changing to negative of the symbol (entries) of each non-zero entries of A.

Let

Then

Hence, B is the Additive Inverse of A.

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