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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 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  and 
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.
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