Matrix have different applications at different places. One can use it in Physics while other can use it in Computer Science for different purposes. 

Basics of Matrices

By definition, a matrix is an arrangment of the numbers, these numbers are called the elements. It is repersented by the capital letter and elements remain with in square brackets.

Some examples of matrices are given below,

Identify the order and type of a matrix

From this A matrix, you can observe the number of rows and columns.

How to read array of the elements? Elements are the numbers of a matrix. Two rows and two columns are shown here. First we writes rows and then columns. For an example; one by three order, it means one row and 3 columns.  

In the below figure,

1.  A is of two by two order, having 4 elements, it means two rows and two columns. This is also called square matix. 
2. B is of three by three order, having 9 elements, it means three rows and three columns. This is also a square.
3. C is of three by one order, having 3 elements, it means three rows and one column. This is not square, because number of rows and number of columns are different. 
4. D is of one by three order, having 3 elements, it means one row and three columns. This is not square, as above said 

Chek order of the matrix and its elements positions.

Additon of Two Matrices

Two matrices A and B of two by two orders are given below. We have to add the elements for the addition of the two matrices. 

For it, add the elements of same positions, in both the matrices to get the resultant matrix. We have added first 2 and 3, then 4 and 5, then 5 and 2 and at the end 7 and 1.

This is the process of addition.  

Multiplication by a constant in Matrix

Constant may be a symbol or a number. When we multiply a matrix with a constant, this constant product we consider with all the elements.

Multiplication of two matrices

The similar way as of the addition, but now we will take products.  Multiplication of matrices of the same order. 

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Subtraction of matrices

Check the order of the matrices, Subtract the second matrix elements from the first matrix elements, as shown in the below picture.

Conclusion

1. Check the order of the matrices first of all
2. Then apply the mathematical operations, like multiplication, addition, subtraction and divisions.
3. Start from the lowest and simple order of the matrix like two by two matrices