We are given with two **matrices A, B **of same order

**and a scalar**

**k**. How to 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 that equation is true.

Lets first prove that and have same order.

Let order of **A** and **B** be **m x n** {They must have same order to be added}

Then, Order of **A+B **would also be **m x n**

Order of would also be equal to **m x n**

Now, find out order of right hand side of equation

We have supposed order of **A** and **B** equal to **m x n**

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

Order of ** **would be equal to** m x n.**

Therefore, and have same order.

Now, lets prove that and have equal corresponding elements.

element of

= element of **A + ** element of **B**}

= k. element of **A + k.** element of **B**

= element of **kA** + element of **KB**

= element of (**kA+kB)**

Therefore, we can say that corresponding elements of and are also equal. We have already proved that their order is same.

Therefore, equation is true.