# Algebra of Matrices

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

Subtraction can be done by taking the 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 the number of columns of matrix is equal to the 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 the corresponding elements of the 1st row of and the 1st column of . Similarly, the element (1,2) position of is obtained by adding the products of the corresponding elements of the 2nd row of and the 2nd column of and so on.

Suppose

__Example__**:**

Let

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

i.e.