The algebra of matrices includes

- Addition of Matrices
- Subtraction of Matrices
- Multiplication of a Matrix by Scalar
- Multiplication of Matrices

__Addition of Matrices__**:**

Two matrices and can be added only if order of matrix is equal to order of matrix .

Then addition of matrices and can be obtained by adding the corresponding elements and . The order of is the same as the order of the order of .

Suppose

Then

__Example__**:**

Let

Then

__Subtraction of Matrices__**:**

Subtraction of two matrices is the similar to the addition of two matrices. Two matrices and are said to be conformable for subtraction , if both and have the same order.

Subtraction can be obtained by taking differences of the corresponding elements of matrices and . The order of is the same as the order of and order of .

Suppose

Then

__Example__**:**

Let

Then

__Multiplication of a Matrix by Scalar__**:**

Let be any given matrix and let be any real number (scalar), then multiplication , of the matrix with the real number is obtained by multiplying each element of the matrix by .

Suppose

Then

__Example__**:**

Let

Then

__Multiplication of Matrices__**:**

Let and be any two given matrices, then the multiplication can be possible only if number of columns of matrix is equal to number of rows of matrix . Then multiplication can be obtained by the following method.

The element (1,1) position of is obtained by adding the products of corresponding elements of 1st row of and 1st column of . Similarly, the element (1,2) position of is obtained by adding the products of corresponding elements of 2nd row of and 2nd column of and so on.

Suppose

__Example__**:**

Let

Since number of columns of is 3 and number of rows of is also 3, So can be found. i.e.