We are given with a **matrix A** and two scalars **k1** and **k2, **how can we prove that ?

**Two matrices** are equal if they have same order and their corresponding elements are equal.

Similarly, if we can prove that and have same order and their corresponding elements are equal then it means equation is true.

Lets first prove that and have same order.

Let order of **matrix A** be **m x n**

Order of would also be **m x n** because is just a scalar.

Now lets calculate order of right hand side of equation .

We have supposed that order of **A** is **m x n**

Order of would be **m x n **and order of would also be equal to **m x n**.

Order of would be **m x n**

Therefore, and have same order.

Now, lets prove that corresponding elements of and are equal.

element of

= . element of **matrix** **A**

= . element of **matrix** **A + **. element of **matrix A**

= element of **matrix** + element of **matrix**

= element of **matrix **(

Therefore, we can say that corresponding elements of and are equal. We have already proved that they have same order. Hence, equation is true.