Addition and Subtraction of Matrices

The operation with any matrix will always result in another matrix, regardless of the operation used.
Before we talk about addition and subtraction of matrices, let's remember what a matrix is ​​formed by: every matrix has its elements that are arranged in rows and columns.
The number of rows and columns must be greater than or equal to 1. Each element is represented with the row and column it belongs to. Example: Given a matrix B of order 2 x 3, the element found in the 1st row and 2nd column will be represented by b₁₂.
►Addition
The matrices involved in the addition must be of the same order. And the result of that sum will also be another matrix with the same order.
So we can conclude that:
If we add matrix A to matrix B of the same order, A + B = C, we will have another matrix C as a result. of the same order and to form the elements of C we will add the corresponding elements of A and B, like this: The₁₁ + b₁₁ = c₁₁.
Examples:
Given the matrix A= 3 x 3 and matrix B= 3 x 3, if we add A + B, we have:

+ = 3 x 3
Note the highlighted elements:
The₁₃ = - 1 and b₁₃ = - 5 when we add these elements we will reach a third which is the
ç₁₃ = -6. Because -1 + (-5) = -1 – 5 = - 6
The same happens with the other elements, to get to the c element₃₂, we had to add the₃₂ + b₃₂. Because, 3 + (-5) = 3 – 5 = - 2
So: A + B = C, where C has the same order as A and B.
►Subtraction
The two matrices involved in the subtraction must be of the same order. And the difference between them should give the answer another matrix, but of the same order.
So we have:
If we subtract matrix A from matrix B of the same order, A – B = C, we get another matrix C of the same order. And to form the elements of C, we'll subtract the elements of A with the corresponding elements of B, like this: The₂₁ - B₂₁ = c₂₁.
Examples:
Given the matrix A = 3 x 3 and B = 3 x 3, if we subtract A - B, we have:
-= 3 x 3
Note the highlighted elements:
When we subtract the₁₃ - B₁₃ = c_13,-1 – (-5) = -1 + 5 = 4
When we subtract the₃₁ - B₃₁ = c_31,- 4 – (-1) = -4 + 1 = -3
So A – B = C, where C is a matrix of the same order as A and B.

by Danielle de Miranda
Graduated in Mathematics
Brazil School Team

Matrix and Determinant - Math - Brazil school

Source: Brazil School - https://brasilescola.uol.com.br/matematica/adicao-subtracao-matrizes.htm