**Simple Operations on Matrices**
Here are some simple operations you can implement on matrices:

*1) Matrix Addition*

Matrices **A** and **B** can be added, if they are the same size (e.g., **m x n**). The matrix sum **C = A + B** also will be a **m x n** matrix, where for each element **c**_{ij} = a_{ij} + b_{ij} and **1 ≤ i ≤ m** and **1 ≤ j ≤ n**.

To add these two matrices:

You would use this solution:

Matrix addition is commutative (e.g., **A + B = B + A**) and associative (e.g., **C + (D + E) = (C + D) + E**).

*2) Matrix Subtraction*

Two matrices (**A** and **B**) can be subtracted if they are the same size (e.g., **k x l**). The matrix difference **D = A – B** will also be a **k x l** matrix with the element **d**_{ij} = a_{ij} – b_{ij}, where **1 ≤ i ≤ k** and **1 ≤ j ≤ l**.

To subtract matrix **B** from matrix **A**:

You would use this solution:

Matrix subtraction is neither commutative nor associative.

*3) Matrix Scalar Multiplication*

If **A** is an **m x n** matrix and the constant **k** is a number, then the scalar product of **k** and **A** is a new matrix **B = kA**, where **b**_{ij} = ka_{ij} and **1 ≤ i ≤ m** and **1 ≤ j ≤ n**.

To find **B = 5∙A**, where:

You would use this solution:

Scalar multiplication is commutative and associative:

```
```**k(AB) = (kA)B = A(kB) = (AB)k**